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| {"metadata":{"kernelspec":{"name":"ir","display_name":"R","language":"R"},"language_info":{"name":"R","codemirror_mode":"r","pygments_lexer":"r","mimetype":"text/x-r-source","file_extension":".r","version":"4.0.5"}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"code","source":"# This R environment comes with many helpful analytics packages installed\n# It is defined by the kaggle/rstats Docker image: https://github.com/kaggle/docker-rstats\n# For example, here's a helpful package to load\n\nlibrary(tidyverse) # metapackage of all tidyverse packages\n\n# Input data files are available in the read-only \"../input/\" directory\n# For example, running this (by clicking run or pressing Shift+Enter) will list all files under the input directory\n\nlist.files(path = \"../input\")\n\n# You can write up to 20GB to the current directory (/kaggle/working/) that gets preserved as output when you create a version using \"Save & Run All\" \n# You can also write temporary files to /kaggle/temp/, but they won't be saved outside of the current session","metadata":{"_uuid":"051d70d956493feee0c6d64651c6a088724dca2a","_execution_state":"idle"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"# # Get data from yahoo finance","metadata":{}},{"cell_type":"code","source":"library(quantmod)\nlibrary(corrplot)\nlibrary(corrgram)\nlibrary(TTR)\nlibrary(caret)\nlibrary(caTools)\nlibrary(ROCR)\nlibrary(ROSE)\nlibrary(pROC)\nlibrary(MASS)\nlibrary(glmnet)\n","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:02:01.296504Z","iopub.execute_input":"2023-02-25T20:02:01.298435Z","iopub.status.idle":"2023-02-25T20:02:01.324710Z"},"trusted":true},"execution_count":222,"outputs":[]},{"cell_type":"code","source":"# dowload stock data for Apple Inc. from yahoo Finance\ngetSymbols(\"AAPL\")\nnames(AAPL)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:02:15.926830Z","iopub.execute_input":"2023-02-25T20:02:15.928400Z","iopub.status.idle":"2023-02-25T20:02:16.841382Z"},"trusted":true},"execution_count":223,"outputs":[{"output_type":"display_data","data":{"text/html":"'AAPL'","text/markdown":"'AAPL'","text/latex":"'AAPL'","text/plain":"[1] \"AAPL\""},"metadata":{}},{"output_type":"display_data","data":{"text/html":"<style>\n.list-inline {list-style: none; margin:0; padding: 0}\n.list-inline>li {display: inline-block}\n.list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n</style>\n<ol class=list-inline><li>'AAPL.Open'</li><li>'AAPL.High'</li><li>'AAPL.Low'</li><li>'AAPL.Close'</li><li>'AAPL.Volume'</li><li>'AAPL.Adjusted'</li></ol>\n","text/markdown":"1. 'AAPL.Open'\n2. 'AAPL.High'\n3. 'AAPL.Low'\n4. 'AAPL.Close'\n5. 'AAPL.Volume'\n6. 'AAPL.Adjusted'\n\n\n","text/latex":"\\begin{enumerate*}\n\\item 'AAPL.Open'\n\\item 'AAPL.High'\n\\item 'AAPL.Low'\n\\item 'AAPL.Close'\n\\item 'AAPL.Volume'\n\\item 'AAPL.Adjusted'\n\\end{enumerate*}\n","text/plain":"[1] \"AAPL.Open\" \"AAPL.High\" \"AAPL.Low\" \"AAPL.Close\" \n[5] \"AAPL.Volume\" \"AAPL.Adjusted\""},"metadata":{}}]},{"cell_type":"code","source":"app <- data.frame(\n date = index(AAPL),\n open = as.numeric(Op(AAPL)),\n close = as.numeric(Cl(AAPL)),\n high = as.numeric(Hi(AAPL)),\n low = as.numeric(Lo(AAPL)),\n volume = as.numeric(Vo(AAPL)))\n# View the extracted data\nhead(app)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:02:19.594203Z","iopub.execute_input":"2023-02-25T20:02:19.595818Z","iopub.status.idle":"2023-02-25T20:02:19.645582Z"},"trusted":true},"execution_count":224,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 6</caption>\n<thead>\n\t<tr><th></th><th scope=col>date</th><th scope=col>open</th><th scope=col>close</th><th scope=col>high</th><th scope=col>low</th><th scope=col>volume</th></tr>\n\t<tr><th></th><th scope=col><date></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>2007-01-03</td><td>3.081786</td><td>2.992857</td><td>3.092143</td><td>2.925000</td><td>1238319600</td></tr>\n\t<tr><th scope=row>2</th><td>2007-01-04</td><td>3.001786</td><td>3.059286</td><td>3.069643</td><td>2.993571</td><td> 847260400</td></tr>\n\t<tr><th scope=row>3</th><td>2007-01-05</td><td>3.063214</td><td>3.037500</td><td>3.078571</td><td>3.014286</td><td> 834741600</td></tr>\n\t<tr><th scope=row>4</th><td>2007-01-08</td><td>3.070000</td><td>3.052500</td><td>3.090357</td><td>3.045714</td><td> 797106800</td></tr>\n\t<tr><th scope=row>5</th><td>2007-01-09</td><td>3.087500</td><td>3.306071</td><td>3.320714</td><td>3.041071</td><td>3349298400</td></tr>\n\t<tr><th scope=row>6</th><td>2007-01-10</td><td>3.383929</td><td>3.464286</td><td>3.492857</td><td>3.337500</td><td>2952880000</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 6\n\n| <!--/--> | date <date> | open <dbl> | close <dbl> | high <dbl> | low <dbl> | volume <dbl> |\n|---|---|---|---|---|---|---|\n| 1 | 2007-01-03 | 3.081786 | 2.992857 | 3.092143 | 2.925000 | 1238319600 |\n| 2 | 2007-01-04 | 3.001786 | 3.059286 | 3.069643 | 2.993571 | 847260400 |\n| 3 | 2007-01-05 | 3.063214 | 3.037500 | 3.078571 | 3.014286 | 834741600 |\n| 4 | 2007-01-08 | 3.070000 | 3.052500 | 3.090357 | 3.045714 | 797106800 |\n| 5 | 2007-01-09 | 3.087500 | 3.306071 | 3.320714 | 3.041071 | 3349298400 |\n| 6 | 2007-01-10 | 3.383929 | 3.464286 | 3.492857 | 3.337500 | 2952880000 |\n\n","text/latex":"A data.frame: 6 × 6\n\\begin{tabular}{r|llllll}\n & date & open & close & high & low & volume\\\\\n & <date> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t1 & 2007-01-03 & 3.081786 & 2.992857 & 3.092143 & 2.925000 & 1238319600\\\\\n\t2 & 2007-01-04 & 3.001786 & 3.059286 & 3.069643 & 2.993571 & 847260400\\\\\n\t3 & 2007-01-05 & 3.063214 & 3.037500 & 3.078571 & 3.014286 & 834741600\\\\\n\t4 & 2007-01-08 & 3.070000 & 3.052500 & 3.090357 & 3.045714 & 797106800\\\\\n\t5 & 2007-01-09 & 3.087500 & 3.306071 & 3.320714 & 3.041071 & 3349298400\\\\\n\t6 & 2007-01-10 & 3.383929 & 3.464286 & 3.492857 & 3.337500 & 2952880000\\\\\n\\end{tabular}\n","text/plain":" date open close high low volume \n1 2007-01-03 3.081786 2.992857 3.092143 2.925000 1238319600\n2 2007-01-04 3.001786 3.059286 3.069643 2.993571 847260400\n3 2007-01-05 3.063214 3.037500 3.078571 3.014286 834741600\n4 2007-01-08 3.070000 3.052500 3.090357 3.045714 797106800\n5 2007-01-09 3.087500 3.306071 3.320714 3.041071 3349298400\n6 2007-01-10 3.383929 3.464286 3.492857 3.337500 2952880000"},"metadata":{}},{"output_type":"display_data","data":{"text/html":"4065","text/markdown":"4065","text/latex":"4065","text/plain":"[1] 4065"},"metadata":{}}]},{"cell_type":"code","source":"# Calculate daily log returns for close price\napp$returns <- c(NA,diff(log(app$close)))\nhead(app)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:02:26.520777Z","iopub.execute_input":"2023-02-25T20:02:26.523132Z","iopub.status.idle":"2023-02-25T20:02:26.568162Z"},"trusted":true},"execution_count":225,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 7</caption>\n<thead>\n\t<tr><th></th><th scope=col>date</th><th scope=col>open</th><th scope=col>close</th><th scope=col>high</th><th scope=col>low</th><th scope=col>volume</th><th scope=col>returns</th></tr>\n\t<tr><th></th><th scope=col><date></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>2007-01-03</td><td>3.081786</td><td>2.992857</td><td>3.092143</td><td>2.925000</td><td>1238319600</td><td> NA</td></tr>\n\t<tr><th scope=row>2</th><td>2007-01-04</td><td>3.001786</td><td>3.059286</td><td>3.069643</td><td>2.993571</td><td> 847260400</td><td> 0.021953106</td></tr>\n\t<tr><th scope=row>3</th><td>2007-01-05</td><td>3.063214</td><td>3.037500</td><td>3.078571</td><td>3.014286</td><td> 834741600</td><td>-0.007146747</td></tr>\n\t<tr><th scope=row>4</th><td>2007-01-08</td><td>3.070000</td><td>3.052500</td><td>3.090357</td><td>3.045714</td><td> 797106800</td><td> 0.004926118</td></tr>\n\t<tr><th scope=row>5</th><td>2007-01-09</td><td>3.087500</td><td>3.306071</td><td>3.320714</td><td>3.041071</td><td>3349298400</td><td> 0.079799548</td></tr>\n\t<tr><th scope=row>6</th><td>2007-01-10</td><td>3.383929</td><td>3.464286</td><td>3.492857</td><td>3.337500</td><td>2952880000</td><td> 0.046746076</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 7\n\n| <!--/--> | date <date> | open <dbl> | close <dbl> | high <dbl> | low <dbl> | volume <dbl> | returns <dbl> |\n|---|---|---|---|---|---|---|---|\n| 1 | 2007-01-03 | 3.081786 | 2.992857 | 3.092143 | 2.925000 | 1238319600 | NA |\n| 2 | 2007-01-04 | 3.001786 | 3.059286 | 3.069643 | 2.993571 | 847260400 | 0.021953106 |\n| 3 | 2007-01-05 | 3.063214 | 3.037500 | 3.078571 | 3.014286 | 834741600 | -0.007146747 |\n| 4 | 2007-01-08 | 3.070000 | 3.052500 | 3.090357 | 3.045714 | 797106800 | 0.004926118 |\n| 5 | 2007-01-09 | 3.087500 | 3.306071 | 3.320714 | 3.041071 | 3349298400 | 0.079799548 |\n| 6 | 2007-01-10 | 3.383929 | 3.464286 | 3.492857 | 3.337500 | 2952880000 | 0.046746076 |\n\n","text/latex":"A data.frame: 6 × 7\n\\begin{tabular}{r|lllllll}\n & date & open & close & high & low & volume & returns\\\\\n & <date> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t1 & 2007-01-03 & 3.081786 & 2.992857 & 3.092143 & 2.925000 & 1238319600 & NA\\\\\n\t2 & 2007-01-04 & 3.001786 & 3.059286 & 3.069643 & 2.993571 & 847260400 & 0.021953106\\\\\n\t3 & 2007-01-05 & 3.063214 & 3.037500 & 3.078571 & 3.014286 & 834741600 & -0.007146747\\\\\n\t4 & 2007-01-08 & 3.070000 & 3.052500 & 3.090357 & 3.045714 & 797106800 & 0.004926118\\\\\n\t5 & 2007-01-09 & 3.087500 & 3.306071 & 3.320714 & 3.041071 & 3349298400 & 0.079799548\\\\\n\t6 & 2007-01-10 & 3.383929 & 3.464286 & 3.492857 & 3.337500 & 2952880000 & 0.046746076\\\\\n\\end{tabular}\n","text/plain":" date open close high low volume returns \n1 2007-01-03 3.081786 2.992857 3.092143 2.925000 1238319600 NA\n2 2007-01-04 3.001786 3.059286 3.069643 2.993571 847260400 0.021953106\n3 2007-01-05 3.063214 3.037500 3.078571 3.014286 834741600 -0.007146747\n4 2007-01-08 3.070000 3.052500 3.090357 3.045714 797106800 0.004926118\n5 2007-01-09 3.087500 3.306071 3.320714 3.041071 3349298400 0.079799548\n6 2007-01-10 3.383929 3.464286 3.492857 3.337500 2952880000 0.046746076"},"metadata":{}}]},{"cell_type":"code","source":" #Create the lags of the log returns\napp$lag1 <-Lag(app$returns, k = 1)\napp$lag2 <- Lag(app$returns, k = 2)\napp$lag3 <- Lag(app$returns, k = 3)\napp$lag4 <- Lag(app$returns, k = 4)\napp$lag5 <- Lag(app$returns, k = 5)\nhead(app)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:02:33.050478Z","iopub.execute_input":"2023-02-25T20:02:33.052012Z","iopub.status.idle":"2023-02-25T20:02:33.094662Z"},"trusted":true},"execution_count":226,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 12</caption>\n<thead>\n\t<tr><th></th><th scope=col>date</th><th scope=col>open</th><th scope=col>close</th><th scope=col>high</th><th scope=col>low</th><th scope=col>volume</th><th scope=col>returns</th><th scope=col>lag1</th><th scope=col>lag2</th><th scope=col>lag3</th><th scope=col>lag4</th><th scope=col>lag5</th></tr>\n\t<tr><th></th><th scope=col><date></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl[,1]></th><th scope=col><dbl[,1]></th><th scope=col><dbl[,1]></th><th scope=col><dbl[,1]></th><th scope=col><dbl[,1]></th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>2007-01-03</td><td>3.081786</td><td>2.992857</td><td>3.092143</td><td>2.925000</td><td>1238319600</td><td> NA</td><td> NA</td><td> NA</td><td> NA</td><td> NA</td><td>NA</td></tr>\n\t<tr><th scope=row>2</th><td>2007-01-04</td><td>3.001786</td><td>3.059286</td><td>3.069643</td><td>2.993571</td><td> 847260400</td><td> 0.021953106</td><td> NA</td><td> NA</td><td> NA</td><td> NA</td><td>NA</td></tr>\n\t<tr><th scope=row>3</th><td>2007-01-05</td><td>3.063214</td><td>3.037500</td><td>3.078571</td><td>3.014286</td><td> 834741600</td><td>-0.007146747</td><td> 0.021953106</td><td> NA</td><td> NA</td><td> NA</td><td>NA</td></tr>\n\t<tr><th scope=row>4</th><td>2007-01-08</td><td>3.070000</td><td>3.052500</td><td>3.090357</td><td>3.045714</td><td> 797106800</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.021953106</td><td> NA</td><td> NA</td><td>NA</td></tr>\n\t<tr><th scope=row>5</th><td>2007-01-09</td><td>3.087500</td><td>3.306071</td><td>3.320714</td><td>3.041071</td><td>3349298400</td><td> 0.079799548</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.021953106</td><td> NA</td><td>NA</td></tr>\n\t<tr><th scope=row>6</th><td>2007-01-10</td><td>3.383929</td><td>3.464286</td><td>3.492857</td><td>3.337500</td><td>2952880000</td><td> 0.046746076</td><td> 0.079799548</td><td> 0.004926118</td><td>-0.007146747</td><td>0.02195311</td><td>NA</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 12\n\n| <!--/--> | date <date> | open <dbl> | close <dbl> | high <dbl> | low <dbl> | volume <dbl> | returns <dbl> | lag1 <dbl[,1]> | lag2 <dbl[,1]> | lag3 <dbl[,1]> | lag4 <dbl[,1]> | lag5 <dbl[,1]> |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| 1 | 2007-01-03 | 3.081786 | 2.992857 | 3.092143 | 2.925000 | 1238319600 | NA | NA | NA | NA | NA | NA |\n| 2 | 2007-01-04 | 3.001786 | 3.059286 | 3.069643 | 2.993571 | 847260400 | 0.021953106 | NA | NA | NA | NA | NA |\n| 3 | 2007-01-05 | 3.063214 | 3.037500 | 3.078571 | 3.014286 | 834741600 | -0.007146747 | 0.021953106 | NA | NA | NA | NA |\n| 4 | 2007-01-08 | 3.070000 | 3.052500 | 3.090357 | 3.045714 | 797106800 | 0.004926118 | -0.007146747 | 0.021953106 | NA | NA | NA |\n| 5 | 2007-01-09 | 3.087500 | 3.306071 | 3.320714 | 3.041071 | 3349298400 | 0.079799548 | 0.004926118 | -0.007146747 | 0.021953106 | NA | NA |\n| 6 | 2007-01-10 | 3.383929 | 3.464286 | 3.492857 | 3.337500 | 2952880000 | 0.046746076 | 0.079799548 | 0.004926118 | -0.007146747 | 0.02195311 | NA |\n\n","text/latex":"A data.frame: 6 × 12\n\\begin{tabular}{r|llllllllllll}\n & date & open & close & high & low & volume & returns & lag1 & lag2 & lag3 & lag4 & lag5\\\\\n & <date> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl{[},1{]}> & <dbl{[},1{]}> & <dbl{[},1{]}> & <dbl{[},1{]}> & <dbl{[},1{]}>\\\\\n\\hline\n\t1 & 2007-01-03 & 3.081786 & 2.992857 & 3.092143 & 2.925000 & 1238319600 & NA & NA & NA & NA & NA & NA\\\\\n\t2 & 2007-01-04 & 3.001786 & 3.059286 & 3.069643 & 2.993571 & 847260400 & 0.021953106 & NA & NA & NA & NA & NA\\\\\n\t3 & 2007-01-05 & 3.063214 & 3.037500 & 3.078571 & 3.014286 & 834741600 & -0.007146747 & 0.021953106 & NA & NA & NA & NA\\\\\n\t4 & 2007-01-08 & 3.070000 & 3.052500 & 3.090357 & 3.045714 & 797106800 & 0.004926118 & -0.007146747 & 0.021953106 & NA & NA & NA\\\\\n\t5 & 2007-01-09 & 3.087500 & 3.306071 & 3.320714 & 3.041071 & 3349298400 & 0.079799548 & 0.004926118 & -0.007146747 & 0.021953106 & NA & NA\\\\\n\t6 & 2007-01-10 & 3.383929 & 3.464286 & 3.492857 & 3.337500 & 2952880000 & 0.046746076 & 0.079799548 & 0.004926118 & -0.007146747 & 0.02195311 & NA\\\\\n\\end{tabular}\n","text/plain":" date open close high low volume returns \n1 2007-01-03 3.081786 2.992857 3.092143 2.925000 1238319600 NA\n2 2007-01-04 3.001786 3.059286 3.069643 2.993571 847260400 0.021953106\n3 2007-01-05 3.063214 3.037500 3.078571 3.014286 834741600 -0.007146747\n4 2007-01-08 3.070000 3.052500 3.090357 3.045714 797106800 0.004926118\n5 2007-01-09 3.087500 3.306071 3.320714 3.041071 3349298400 0.079799548\n6 2007-01-10 3.383929 3.464286 3.492857 3.337500 2952880000 0.046746076\n lag1 lag2 lag3 lag4 lag5\n1 NA NA NA NA NA \n2 NA NA NA NA NA \n3 0.021953106 NA NA NA NA \n4 -0.007146747 0.021953106 NA NA NA \n5 0.004926118 -0.007146747 0.021953106 NA NA \n6 0.079799548 0.004926118 -0.007146747 0.02195311 NA "},"metadata":{}}]},{"cell_type":"code","source":"#Create some other indicators\n# Calculate the rolling standard deviation and mean of close prices\napp$roll_sd <- rollapply(app$close, width = 10, FUN = sd,fill = NA,align = \"right\")\napp$roll_mean <- rollapply(app$close, width = 10, FUN = mean,fill = NA,align = \"right\")\n# Calculate the 10-day and 20-day simple moving averages\napp$ma10 <- SMA(app$close, n = 10)\napp$ma20 <- SMA(app$close, n = 20)\nhead(app)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:02:39.912253Z","iopub.execute_input":"2023-02-25T20:02:39.913707Z","iopub.status.idle":"2023-02-25T20:02:40.052572Z"},"trusted":true},"execution_count":227,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 16</caption>\n<thead>\n\t<tr><th></th><th scope=col>date</th><th scope=col>open</th><th scope=col>close</th><th scope=col>high</th><th scope=col>low</th><th scope=col>volume</th><th scope=col>returns</th><th scope=col>lag1</th><th scope=col>lag2</th><th scope=col>lag3</th><th scope=col>lag4</th><th scope=col>lag5</th><th scope=col>roll_sd</th><th scope=col>roll_mean</th><th scope=col>ma10</th><th scope=col>ma20</th></tr>\n\t<tr><th></th><th scope=col><date></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl[,1]></th><th scope=col><dbl[,1]></th><th scope=col><dbl[,1]></th><th scope=col><dbl[,1]></th><th scope=col><dbl[,1]></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>2007-01-03</td><td>3.081786</td><td>2.992857</td><td>3.092143</td><td>2.925000</td><td>1238319600</td><td> NA</td><td> NA</td><td> NA</td><td> NA</td><td> NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n\t<tr><th scope=row>2</th><td>2007-01-04</td><td>3.001786</td><td>3.059286</td><td>3.069643</td><td>2.993571</td><td> 847260400</td><td> 0.021953106</td><td> NA</td><td> NA</td><td> NA</td><td> NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n\t<tr><th scope=row>3</th><td>2007-01-05</td><td>3.063214</td><td>3.037500</td><td>3.078571</td><td>3.014286</td><td> 834741600</td><td>-0.007146747</td><td> 0.021953106</td><td> NA</td><td> NA</td><td> NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n\t<tr><th scope=row>4</th><td>2007-01-08</td><td>3.070000</td><td>3.052500</td><td>3.090357</td><td>3.045714</td><td> 797106800</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.021953106</td><td> NA</td><td> NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n\t<tr><th scope=row>5</th><td>2007-01-09</td><td>3.087500</td><td>3.306071</td><td>3.320714</td><td>3.041071</td><td>3349298400</td><td> 0.079799548</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.021953106</td><td> NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n\t<tr><th scope=row>6</th><td>2007-01-10</td><td>3.383929</td><td>3.464286</td><td>3.492857</td><td>3.337500</td><td>2952880000</td><td> 0.046746076</td><td> 0.079799548</td><td> 0.004926118</td><td>-0.007146747</td><td>0.02195311</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 16\n\n| <!--/--> | date <date> | open <dbl> | close <dbl> | high <dbl> | low <dbl> | volume <dbl> | returns <dbl> | lag1 <dbl[,1]> | lag2 <dbl[,1]> | lag3 <dbl[,1]> | lag4 <dbl[,1]> | lag5 <dbl[,1]> | roll_sd <dbl> | roll_mean <dbl> | ma10 <dbl> | ma20 <dbl> |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| 1 | 2007-01-03 | 3.081786 | 2.992857 | 3.092143 | 2.925000 | 1238319600 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |\n| 2 | 2007-01-04 | 3.001786 | 3.059286 | 3.069643 | 2.993571 | 847260400 | 0.021953106 | NA | NA | NA | NA | NA | NA | NA | NA | NA |\n| 3 | 2007-01-05 | 3.063214 | 3.037500 | 3.078571 | 3.014286 | 834741600 | -0.007146747 | 0.021953106 | NA | NA | NA | NA | NA | NA | NA | NA |\n| 4 | 2007-01-08 | 3.070000 | 3.052500 | 3.090357 | 3.045714 | 797106800 | 0.004926118 | -0.007146747 | 0.021953106 | NA | NA | NA | NA | NA | NA | NA |\n| 5 | 2007-01-09 | 3.087500 | 3.306071 | 3.320714 | 3.041071 | 3349298400 | 0.079799548 | 0.004926118 | -0.007146747 | 0.021953106 | NA | NA | NA | NA | NA | NA |\n| 6 | 2007-01-10 | 3.383929 | 3.464286 | 3.492857 | 3.337500 | 2952880000 | 0.046746076 | 0.079799548 | 0.004926118 | -0.007146747 | 0.02195311 | NA | NA | NA | NA | NA |\n\n","text/latex":"A data.frame: 6 × 16\n\\begin{tabular}{r|llllllllllllllll}\n & date & open & close & high & low & volume & returns & lag1 & lag2 & lag3 & lag4 & lag5 & roll\\_sd & roll\\_mean & ma10 & ma20\\\\\n & <date> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl{[},1{]}> & <dbl{[},1{]}> & <dbl{[},1{]}> & <dbl{[},1{]}> & <dbl{[},1{]}> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t1 & 2007-01-03 & 3.081786 & 2.992857 & 3.092143 & 2.925000 & 1238319600 & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA\\\\\n\t2 & 2007-01-04 & 3.001786 & 3.059286 & 3.069643 & 2.993571 & 847260400 & 0.021953106 & NA & NA & NA & NA & NA & NA & NA & NA & NA\\\\\n\t3 & 2007-01-05 & 3.063214 & 3.037500 & 3.078571 & 3.014286 & 834741600 & -0.007146747 & 0.021953106 & NA & NA & NA & NA & NA & NA & NA & NA\\\\\n\t4 & 2007-01-08 & 3.070000 & 3.052500 & 3.090357 & 3.045714 & 797106800 & 0.004926118 & -0.007146747 & 0.021953106 & NA & NA & NA & NA & NA & NA & NA\\\\\n\t5 & 2007-01-09 & 3.087500 & 3.306071 & 3.320714 & 3.041071 & 3349298400 & 0.079799548 & 0.004926118 & -0.007146747 & 0.021953106 & NA & NA & NA & NA & NA & NA\\\\\n\t6 & 2007-01-10 & 3.383929 & 3.464286 & 3.492857 & 3.337500 & 2952880000 & 0.046746076 & 0.079799548 & 0.004926118 & -0.007146747 & 0.02195311 & NA & NA & NA & NA & NA\\\\\n\\end{tabular}\n","text/plain":" date open close high low volume returns \n1 2007-01-03 3.081786 2.992857 3.092143 2.925000 1238319600 NA\n2 2007-01-04 3.001786 3.059286 3.069643 2.993571 847260400 0.021953106\n3 2007-01-05 3.063214 3.037500 3.078571 3.014286 834741600 -0.007146747\n4 2007-01-08 3.070000 3.052500 3.090357 3.045714 797106800 0.004926118\n5 2007-01-09 3.087500 3.306071 3.320714 3.041071 3349298400 0.079799548\n6 2007-01-10 3.383929 3.464286 3.492857 3.337500 2952880000 0.046746076\n lag1 lag2 lag3 lag4 lag5 roll_sd roll_mean ma10\n1 NA NA NA NA NA NA NA NA \n2 NA NA NA NA NA NA NA NA \n3 0.021953106 NA NA NA NA NA NA NA \n4 -0.007146747 0.021953106 NA NA NA NA NA NA \n5 0.004926118 -0.007146747 0.021953106 NA NA NA NA NA \n6 0.079799548 0.004926118 -0.007146747 0.02195311 NA NA NA NA \n ma20\n1 NA \n2 NA \n3 NA \n4 NA \n5 NA \n6 NA "},"metadata":{}}]},{"cell_type":"markdown","source":"# Replace NA values in the data using either linear interpolation or spline interpolation","metadata":{}},{"cell_type":"markdown","source":"we use the na.spline() function from the zoo package to fill NA values in the lagged_returns series using spline interpolation. The na.rm = FALSE argument tells the function to keep the NA values in the output series, rather than removing them.","metadata":{}},{"cell_type":"code","source":"# Specify the column indices to interpolate\ncols_to_interp <- c(7:16)\n# Apply na.spline() to the specified columns of the data frame\napp[ ,cols_to_interp] <- apply(app[ ,cols_to_interp], 2, function(x) na.spline(x, na.rm = FALSE))\nhead(app)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:02:48.022463Z","iopub.execute_input":"2023-02-25T20:02:48.023962Z","iopub.status.idle":"2023-02-25T20:02:48.078322Z"},"trusted":true},"execution_count":228,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 16</caption>\n<thead>\n\t<tr><th></th><th scope=col>date</th><th scope=col>open</th><th scope=col>close</th><th scope=col>high</th><th scope=col>low</th><th scope=col>volume</th><th scope=col>returns</th><th scope=col>lag1</th><th scope=col>lag2</th><th scope=col>lag3</th><th scope=col>lag4</th><th scope=col>lag5</th><th scope=col>roll_sd</th><th scope=col>roll_mean</th><th scope=col>ma10</th><th scope=col>ma20</th></tr>\n\t<tr><th></th><th scope=col><date></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>2007-01-03</td><td>3.081786</td><td>2.992857</td><td>3.092143</td><td>2.925000</td><td>1238319600</td><td> 0.055959727</td><td> 0.073245269</td><td> 0.052181885</td><td>-0.028858272</td><td>-0.19150305</td><td>-0.45738030</td><td>1.9662026</td><td>1.910904</td><td>1.910904</td><td>-1.4032928</td></tr>\n\t<tr><th scope=row>2</th><td>2007-01-04</td><td>3.001786</td><td>3.059286</td><td>3.069643</td><td>2.993571</td><td> 847260400</td><td> 0.021953106</td><td> 0.055959727</td><td> 0.073245269</td><td> 0.052181885</td><td>-0.02885827</td><td>-0.19150305</td><td>1.5437420</td><td>2.222110</td><td>2.222110</td><td>-0.7790927</td></tr>\n\t<tr><th scope=row>3</th><td>2007-01-05</td><td>3.063214</td><td>3.037500</td><td>3.078571</td><td>3.014286</td><td> 834741600</td><td>-0.007146747</td><td> 0.021953106</td><td> 0.055959727</td><td> 0.073245269</td><td> 0.05218189</td><td>-0.02885827</td><td>1.1942124</td><td>2.481829</td><td>2.481829</td><td>-0.2141749</td></tr>\n\t<tr><th scope=row>4</th><td>2007-01-08</td><td>3.070000</td><td>3.052500</td><td>3.090357</td><td>3.045714</td><td> 797106800</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.021953106</td><td> 0.055959727</td><td> 0.07324527</td><td> 0.05218189</td><td>0.9105575</td><td>2.694810</td><td>2.694810</td><td> 0.2944070</td></tr>\n\t<tr><th scope=row>5</th><td>2007-01-09</td><td>3.087500</td><td>3.306071</td><td>3.320714</td><td>3.041071</td><td>3349298400</td><td> 0.079799548</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.021953106</td><td> 0.05595973</td><td> 0.07324527</td><td>0.6857206</td><td>2.865803</td><td>2.865803</td><td> 0.7495994</td></tr>\n\t<tr><th scope=row>6</th><td>2007-01-10</td><td>3.383929</td><td>3.464286</td><td>3.492857</td><td>3.337500</td><td>2952880000</td><td> 0.046746076</td><td> 0.079799548</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.02195311</td><td> 0.05595973</td><td>0.5126451</td><td>2.999560</td><td>2.999560</td><td> 1.1543489</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 16\n\n| <!--/--> | date <date> | open <dbl> | close <dbl> | high <dbl> | low <dbl> | volume <dbl> | returns <dbl> | lag1 <dbl> | lag2 <dbl> | lag3 <dbl> | lag4 <dbl> | lag5 <dbl> | roll_sd <dbl> | roll_mean <dbl> | ma10 <dbl> | ma20 <dbl> |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| 1 | 2007-01-03 | 3.081786 | 2.992857 | 3.092143 | 2.925000 | 1238319600 | 0.055959727 | 0.073245269 | 0.052181885 | -0.028858272 | -0.19150305 | -0.45738030 | 1.9662026 | 1.910904 | 1.910904 | -1.4032928 |\n| 2 | 2007-01-04 | 3.001786 | 3.059286 | 3.069643 | 2.993571 | 847260400 | 0.021953106 | 0.055959727 | 0.073245269 | 0.052181885 | -0.02885827 | -0.19150305 | 1.5437420 | 2.222110 | 2.222110 | -0.7790927 |\n| 3 | 2007-01-05 | 3.063214 | 3.037500 | 3.078571 | 3.014286 | 834741600 | -0.007146747 | 0.021953106 | 0.055959727 | 0.073245269 | 0.05218189 | -0.02885827 | 1.1942124 | 2.481829 | 2.481829 | -0.2141749 |\n| 4 | 2007-01-08 | 3.070000 | 3.052500 | 3.090357 | 3.045714 | 797106800 | 0.004926118 | -0.007146747 | 0.021953106 | 0.055959727 | 0.07324527 | 0.05218189 | 0.9105575 | 2.694810 | 2.694810 | 0.2944070 |\n| 5 | 2007-01-09 | 3.087500 | 3.306071 | 3.320714 | 3.041071 | 3349298400 | 0.079799548 | 0.004926118 | -0.007146747 | 0.021953106 | 0.05595973 | 0.07324527 | 0.6857206 | 2.865803 | 2.865803 | 0.7495994 |\n| 6 | 2007-01-10 | 3.383929 | 3.464286 | 3.492857 | 3.337500 | 2952880000 | 0.046746076 | 0.079799548 | 0.004926118 | -0.007146747 | 0.02195311 | 0.05595973 | 0.5126451 | 2.999560 | 2.999560 | 1.1543489 |\n\n","text/latex":"A data.frame: 6 × 16\n\\begin{tabular}{r|llllllllllllllll}\n & date & open & close & high & low & volume & returns & lag1 & lag2 & lag3 & lag4 & lag5 & roll\\_sd & roll\\_mean & ma10 & ma20\\\\\n & <date> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t1 & 2007-01-03 & 3.081786 & 2.992857 & 3.092143 & 2.925000 & 1238319600 & 0.055959727 & 0.073245269 & 0.052181885 & -0.028858272 & -0.19150305 & -0.45738030 & 1.9662026 & 1.910904 & 1.910904 & -1.4032928\\\\\n\t2 & 2007-01-04 & 3.001786 & 3.059286 & 3.069643 & 2.993571 & 847260400 & 0.021953106 & 0.055959727 & 0.073245269 & 0.052181885 & -0.02885827 & -0.19150305 & 1.5437420 & 2.222110 & 2.222110 & -0.7790927\\\\\n\t3 & 2007-01-05 & 3.063214 & 3.037500 & 3.078571 & 3.014286 & 834741600 & -0.007146747 & 0.021953106 & 0.055959727 & 0.073245269 & 0.05218189 & -0.02885827 & 1.1942124 & 2.481829 & 2.481829 & -0.2141749\\\\\n\t4 & 2007-01-08 & 3.070000 & 3.052500 & 3.090357 & 3.045714 & 797106800 & 0.004926118 & -0.007146747 & 0.021953106 & 0.055959727 & 0.07324527 & 0.05218189 & 0.9105575 & 2.694810 & 2.694810 & 0.2944070\\\\\n\t5 & 2007-01-09 & 3.087500 & 3.306071 & 3.320714 & 3.041071 & 3349298400 & 0.079799548 & 0.004926118 & -0.007146747 & 0.021953106 & 0.05595973 & 0.07324527 & 0.6857206 & 2.865803 & 2.865803 & 0.7495994\\\\\n\t6 & 2007-01-10 & 3.383929 & 3.464286 & 3.492857 & 3.337500 & 2952880000 & 0.046746076 & 0.079799548 & 0.004926118 & -0.007146747 & 0.02195311 & 0.05595973 & 0.5126451 & 2.999560 & 2.999560 & 1.1543489\\\\\n\\end{tabular}\n","text/plain":" date open close high low volume returns \n1 2007-01-03 3.081786 2.992857 3.092143 2.925000 1238319600 0.055959727\n2 2007-01-04 3.001786 3.059286 3.069643 2.993571 847260400 0.021953106\n3 2007-01-05 3.063214 3.037500 3.078571 3.014286 834741600 -0.007146747\n4 2007-01-08 3.070000 3.052500 3.090357 3.045714 797106800 0.004926118\n5 2007-01-09 3.087500 3.306071 3.320714 3.041071 3349298400 0.079799548\n6 2007-01-10 3.383929 3.464286 3.492857 3.337500 2952880000 0.046746076\n lag1 lag2 lag3 lag4 lag5 roll_sd \n1 0.073245269 0.052181885 -0.028858272 -0.19150305 -0.45738030 1.9662026\n2 0.055959727 0.073245269 0.052181885 -0.02885827 -0.19150305 1.5437420\n3 0.021953106 0.055959727 0.073245269 0.05218189 -0.02885827 1.1942124\n4 -0.007146747 0.021953106 0.055959727 0.07324527 0.05218189 0.9105575\n5 0.004926118 -0.007146747 0.021953106 0.05595973 0.07324527 0.6857206\n6 0.079799548 0.004926118 -0.007146747 0.02195311 0.05595973 0.5126451\n roll_mean ma10 ma20 \n1 1.910904 1.910904 -1.4032928\n2 2.222110 2.222110 -0.7790927\n3 2.481829 2.481829 -0.2141749\n4 2.694810 2.694810 0.2944070\n5 2.865803 2.865803 0.7495994\n6 2.999560 2.999560 1.1543489"},"metadata":{}}]},{"cell_type":"markdown","source":"# # Creating Direction variable","metadata":{}},{"cell_type":"markdown","source":"**To create a \"Direction\" variable for returns, you can assign a value of 1 if the returns are positive and 0 if the returns are negative. An alternative approach is to use the labels \"UP\" and \"DOWN\" instead of 1 and 0 to indicate the direction of the returns.**","metadata":{}},{"cell_type":"code","source":"#create Direction variables for returns movement\napp$Direction<-ifelse(app$returns>=0,\"1\",\"0\")\nhead(app)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:02:54.918298Z","iopub.execute_input":"2023-02-25T20:02:54.919820Z","iopub.status.idle":"2023-02-25T20:02:54.955353Z"},"trusted":true},"execution_count":229,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 17</caption>\n<thead>\n\t<tr><th></th><th scope=col>date</th><th scope=col>open</th><th scope=col>close</th><th scope=col>high</th><th scope=col>low</th><th scope=col>volume</th><th scope=col>returns</th><th scope=col>lag1</th><th scope=col>lag2</th><th scope=col>lag3</th><th scope=col>lag4</th><th scope=col>lag5</th><th scope=col>roll_sd</th><th scope=col>roll_mean</th><th scope=col>ma10</th><th scope=col>ma20</th><th scope=col>Direction</th></tr>\n\t<tr><th></th><th scope=col><date></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><chr></th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>2007-01-03</td><td>3.081786</td><td>2.992857</td><td>3.092143</td><td>2.925000</td><td>1238319600</td><td> 0.055959727</td><td> 0.073245269</td><td> 0.052181885</td><td>-0.028858272</td><td>-0.19150305</td><td>-0.45738030</td><td>1.9662026</td><td>1.910904</td><td>1.910904</td><td>-1.4032928</td><td>1</td></tr>\n\t<tr><th scope=row>2</th><td>2007-01-04</td><td>3.001786</td><td>3.059286</td><td>3.069643</td><td>2.993571</td><td> 847260400</td><td> 0.021953106</td><td> 0.055959727</td><td> 0.073245269</td><td> 0.052181885</td><td>-0.02885827</td><td>-0.19150305</td><td>1.5437420</td><td>2.222110</td><td>2.222110</td><td>-0.7790927</td><td>1</td></tr>\n\t<tr><th scope=row>3</th><td>2007-01-05</td><td>3.063214</td><td>3.037500</td><td>3.078571</td><td>3.014286</td><td> 834741600</td><td>-0.007146747</td><td> 0.021953106</td><td> 0.055959727</td><td> 0.073245269</td><td> 0.05218189</td><td>-0.02885827</td><td>1.1942124</td><td>2.481829</td><td>2.481829</td><td>-0.2141749</td><td>0</td></tr>\n\t<tr><th scope=row>4</th><td>2007-01-08</td><td>3.070000</td><td>3.052500</td><td>3.090357</td><td>3.045714</td><td> 797106800</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.021953106</td><td> 0.055959727</td><td> 0.07324527</td><td> 0.05218189</td><td>0.9105575</td><td>2.694810</td><td>2.694810</td><td> 0.2944070</td><td>1</td></tr>\n\t<tr><th scope=row>5</th><td>2007-01-09</td><td>3.087500</td><td>3.306071</td><td>3.320714</td><td>3.041071</td><td>3349298400</td><td> 0.079799548</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.021953106</td><td> 0.05595973</td><td> 0.07324527</td><td>0.6857206</td><td>2.865803</td><td>2.865803</td><td> 0.7495994</td><td>1</td></tr>\n\t<tr><th scope=row>6</th><td>2007-01-10</td><td>3.383929</td><td>3.464286</td><td>3.492857</td><td>3.337500</td><td>2952880000</td><td> 0.046746076</td><td> 0.079799548</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.02195311</td><td> 0.05595973</td><td>0.5126451</td><td>2.999560</td><td>2.999560</td><td> 1.1543489</td><td>1</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 17\n\n| <!--/--> | date <date> | open <dbl> | close <dbl> | high <dbl> | low <dbl> | volume <dbl> | returns <dbl> | lag1 <dbl> | lag2 <dbl> | lag3 <dbl> | lag4 <dbl> | lag5 <dbl> | roll_sd <dbl> | roll_mean <dbl> | ma10 <dbl> | ma20 <dbl> | Direction <chr> |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| 1 | 2007-01-03 | 3.081786 | 2.992857 | 3.092143 | 2.925000 | 1238319600 | 0.055959727 | 0.073245269 | 0.052181885 | -0.028858272 | -0.19150305 | -0.45738030 | 1.9662026 | 1.910904 | 1.910904 | -1.4032928 | 1 |\n| 2 | 2007-01-04 | 3.001786 | 3.059286 | 3.069643 | 2.993571 | 847260400 | 0.021953106 | 0.055959727 | 0.073245269 | 0.052181885 | -0.02885827 | -0.19150305 | 1.5437420 | 2.222110 | 2.222110 | -0.7790927 | 1 |\n| 3 | 2007-01-05 | 3.063214 | 3.037500 | 3.078571 | 3.014286 | 834741600 | -0.007146747 | 0.021953106 | 0.055959727 | 0.073245269 | 0.05218189 | -0.02885827 | 1.1942124 | 2.481829 | 2.481829 | -0.2141749 | 0 |\n| 4 | 2007-01-08 | 3.070000 | 3.052500 | 3.090357 | 3.045714 | 797106800 | 0.004926118 | -0.007146747 | 0.021953106 | 0.055959727 | 0.07324527 | 0.05218189 | 0.9105575 | 2.694810 | 2.694810 | 0.2944070 | 1 |\n| 5 | 2007-01-09 | 3.087500 | 3.306071 | 3.320714 | 3.041071 | 3349298400 | 0.079799548 | 0.004926118 | -0.007146747 | 0.021953106 | 0.05595973 | 0.07324527 | 0.6857206 | 2.865803 | 2.865803 | 0.7495994 | 1 |\n| 6 | 2007-01-10 | 3.383929 | 3.464286 | 3.492857 | 3.337500 | 2952880000 | 0.046746076 | 0.079799548 | 0.004926118 | -0.007146747 | 0.02195311 | 0.05595973 | 0.5126451 | 2.999560 | 2.999560 | 1.1543489 | 1 |\n\n","text/latex":"A data.frame: 6 × 17\n\\begin{tabular}{r|lllllllllllllllll}\n & date & open & close & high & low & volume & returns & lag1 & lag2 & lag3 & lag4 & lag5 & roll\\_sd & roll\\_mean & ma10 & ma20 & Direction\\\\\n & <date> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <chr>\\\\\n\\hline\n\t1 & 2007-01-03 & 3.081786 & 2.992857 & 3.092143 & 2.925000 & 1238319600 & 0.055959727 & 0.073245269 & 0.052181885 & -0.028858272 & -0.19150305 & -0.45738030 & 1.9662026 & 1.910904 & 1.910904 & -1.4032928 & 1\\\\\n\t2 & 2007-01-04 & 3.001786 & 3.059286 & 3.069643 & 2.993571 & 847260400 & 0.021953106 & 0.055959727 & 0.073245269 & 0.052181885 & -0.02885827 & -0.19150305 & 1.5437420 & 2.222110 & 2.222110 & -0.7790927 & 1\\\\\n\t3 & 2007-01-05 & 3.063214 & 3.037500 & 3.078571 & 3.014286 & 834741600 & -0.007146747 & 0.021953106 & 0.055959727 & 0.073245269 & 0.05218189 & -0.02885827 & 1.1942124 & 2.481829 & 2.481829 & -0.2141749 & 0\\\\\n\t4 & 2007-01-08 & 3.070000 & 3.052500 & 3.090357 & 3.045714 & 797106800 & 0.004926118 & -0.007146747 & 0.021953106 & 0.055959727 & 0.07324527 & 0.05218189 & 0.9105575 & 2.694810 & 2.694810 & 0.2944070 & 1\\\\\n\t5 & 2007-01-09 & 3.087500 & 3.306071 & 3.320714 & 3.041071 & 3349298400 & 0.079799548 & 0.004926118 & -0.007146747 & 0.021953106 & 0.05595973 & 0.07324527 & 0.6857206 & 2.865803 & 2.865803 & 0.7495994 & 1\\\\\n\t6 & 2007-01-10 & 3.383929 & 3.464286 & 3.492857 & 3.337500 & 2952880000 & 0.046746076 & 0.079799548 & 0.004926118 & -0.007146747 & 0.02195311 & 0.05595973 & 0.5126451 & 2.999560 & 2.999560 & 1.1543489 & 1\\\\\n\\end{tabular}\n","text/plain":" date open close high low volume returns \n1 2007-01-03 3.081786 2.992857 3.092143 2.925000 1238319600 0.055959727\n2 2007-01-04 3.001786 3.059286 3.069643 2.993571 847260400 0.021953106\n3 2007-01-05 3.063214 3.037500 3.078571 3.014286 834741600 -0.007146747\n4 2007-01-08 3.070000 3.052500 3.090357 3.045714 797106800 0.004926118\n5 2007-01-09 3.087500 3.306071 3.320714 3.041071 3349298400 0.079799548\n6 2007-01-10 3.383929 3.464286 3.492857 3.337500 2952880000 0.046746076\n lag1 lag2 lag3 lag4 lag5 roll_sd \n1 0.073245269 0.052181885 -0.028858272 -0.19150305 -0.45738030 1.9662026\n2 0.055959727 0.073245269 0.052181885 -0.02885827 -0.19150305 1.5437420\n3 0.021953106 0.055959727 0.073245269 0.05218189 -0.02885827 1.1942124\n4 -0.007146747 0.021953106 0.055959727 0.07324527 0.05218189 0.9105575\n5 0.004926118 -0.007146747 0.021953106 0.05595973 0.07324527 0.6857206\n6 0.079799548 0.004926118 -0.007146747 0.02195311 0.05595973 0.5126451\n roll_mean ma10 ma20 Direction\n1 1.910904 1.910904 -1.4032928 1 \n2 2.222110 2.222110 -0.7790927 1 \n3 2.481829 2.481829 -0.2141749 0 \n4 2.694810 2.694810 0.2944070 1 \n5 2.865803 2.865803 0.7495994 1 \n6 2.999560 2.999560 1.1543489 1 "},"metadata":{}}]},{"cell_type":"markdown","source":"# Creat a Sub data set","metadata":{}},{"cell_type":"code","source":"app_sub <- app[, c(\"volume\", names(app)[8:17])]\nhead(app_sub)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:03:09.084213Z","iopub.execute_input":"2023-02-25T20:03:09.085838Z","iopub.status.idle":"2023-02-25T20:03:09.117358Z"},"trusted":true},"execution_count":230,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 11</caption>\n<thead>\n\t<tr><th></th><th scope=col>volume</th><th scope=col>lag1</th><th scope=col>lag2</th><th scope=col>lag3</th><th scope=col>lag4</th><th scope=col>lag5</th><th scope=col>roll_sd</th><th scope=col>roll_mean</th><th scope=col>ma10</th><th scope=col>ma20</th><th scope=col>Direction</th></tr>\n\t<tr><th></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><chr></th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>1238319600</td><td> 0.073245269</td><td> 0.052181885</td><td>-0.028858272</td><td>-0.19150305</td><td>-0.45738030</td><td>1.9662026</td><td>1.910904</td><td>1.910904</td><td>-1.4032928</td><td>1</td></tr>\n\t<tr><th scope=row>2</th><td> 847260400</td><td> 0.055959727</td><td> 0.073245269</td><td> 0.052181885</td><td>-0.02885827</td><td>-0.19150305</td><td>1.5437420</td><td>2.222110</td><td>2.222110</td><td>-0.7790927</td><td>1</td></tr>\n\t<tr><th scope=row>3</th><td> 834741600</td><td> 0.021953106</td><td> 0.055959727</td><td> 0.073245269</td><td> 0.05218189</td><td>-0.02885827</td><td>1.1942124</td><td>2.481829</td><td>2.481829</td><td>-0.2141749</td><td>0</td></tr>\n\t<tr><th scope=row>4</th><td> 797106800</td><td>-0.007146747</td><td> 0.021953106</td><td> 0.055959727</td><td> 0.07324527</td><td> 0.05218189</td><td>0.9105575</td><td>2.694810</td><td>2.694810</td><td> 0.2944070</td><td>1</td></tr>\n\t<tr><th scope=row>5</th><td>3349298400</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.021953106</td><td> 0.05595973</td><td> 0.07324527</td><td>0.6857206</td><td>2.865803</td><td>2.865803</td><td> 0.7495994</td><td>1</td></tr>\n\t<tr><th scope=row>6</th><td>2952880000</td><td> 0.079799548</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.02195311</td><td> 0.05595973</td><td>0.5126451</td><td>2.999560</td><td>2.999560</td><td> 1.1543489</td><td>1</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 11\n\n| <!--/--> | volume <dbl> | lag1 <dbl> | lag2 <dbl> | lag3 <dbl> | lag4 <dbl> | lag5 <dbl> | roll_sd <dbl> | roll_mean <dbl> | ma10 <dbl> | ma20 <dbl> | Direction <chr> |\n|---|---|---|---|---|---|---|---|---|---|---|---|\n| 1 | 1238319600 | 0.073245269 | 0.052181885 | -0.028858272 | -0.19150305 | -0.45738030 | 1.9662026 | 1.910904 | 1.910904 | -1.4032928 | 1 |\n| 2 | 847260400 | 0.055959727 | 0.073245269 | 0.052181885 | -0.02885827 | -0.19150305 | 1.5437420 | 2.222110 | 2.222110 | -0.7790927 | 1 |\n| 3 | 834741600 | 0.021953106 | 0.055959727 | 0.073245269 | 0.05218189 | -0.02885827 | 1.1942124 | 2.481829 | 2.481829 | -0.2141749 | 0 |\n| 4 | 797106800 | -0.007146747 | 0.021953106 | 0.055959727 | 0.07324527 | 0.05218189 | 0.9105575 | 2.694810 | 2.694810 | 0.2944070 | 1 |\n| 5 | 3349298400 | 0.004926118 | -0.007146747 | 0.021953106 | 0.05595973 | 0.07324527 | 0.6857206 | 2.865803 | 2.865803 | 0.7495994 | 1 |\n| 6 | 2952880000 | 0.079799548 | 0.004926118 | -0.007146747 | 0.02195311 | 0.05595973 | 0.5126451 | 2.999560 | 2.999560 | 1.1543489 | 1 |\n\n","text/latex":"A data.frame: 6 × 11\n\\begin{tabular}{r|lllllllllll}\n & volume & lag1 & lag2 & lag3 & lag4 & lag5 & roll\\_sd & roll\\_mean & ma10 & ma20 & Direction\\\\\n & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <chr>\\\\\n\\hline\n\t1 & 1238319600 & 0.073245269 & 0.052181885 & -0.028858272 & -0.19150305 & -0.45738030 & 1.9662026 & 1.910904 & 1.910904 & -1.4032928 & 1\\\\\n\t2 & 847260400 & 0.055959727 & 0.073245269 & 0.052181885 & -0.02885827 & -0.19150305 & 1.5437420 & 2.222110 & 2.222110 & -0.7790927 & 1\\\\\n\t3 & 834741600 & 0.021953106 & 0.055959727 & 0.073245269 & 0.05218189 & -0.02885827 & 1.1942124 & 2.481829 & 2.481829 & -0.2141749 & 0\\\\\n\t4 & 797106800 & -0.007146747 & 0.021953106 & 0.055959727 & 0.07324527 & 0.05218189 & 0.9105575 & 2.694810 & 2.694810 & 0.2944070 & 1\\\\\n\t5 & 3349298400 & 0.004926118 & -0.007146747 & 0.021953106 & 0.05595973 & 0.07324527 & 0.6857206 & 2.865803 & 2.865803 & 0.7495994 & 1\\\\\n\t6 & 2952880000 & 0.079799548 & 0.004926118 & -0.007146747 & 0.02195311 & 0.05595973 & 0.5126451 & 2.999560 & 2.999560 & 1.1543489 & 1\\\\\n\\end{tabular}\n","text/plain":" volume lag1 lag2 lag3 lag4 lag5 \n1 1238319600 0.073245269 0.052181885 -0.028858272 -0.19150305 -0.45738030\n2 847260400 0.055959727 0.073245269 0.052181885 -0.02885827 -0.19150305\n3 834741600 0.021953106 0.055959727 0.073245269 0.05218189 -0.02885827\n4 797106800 -0.007146747 0.021953106 0.055959727 0.07324527 0.05218189\n5 3349298400 0.004926118 -0.007146747 0.021953106 0.05595973 0.07324527\n6 2952880000 0.079799548 0.004926118 -0.007146747 0.02195311 0.05595973\n roll_sd roll_mean ma10 ma20 Direction\n1 1.9662026 1.910904 1.910904 -1.4032928 1 \n2 1.5437420 2.222110 2.222110 -0.7790927 1 \n3 1.1942124 2.481829 2.481829 -0.2141749 0 \n4 0.9105575 2.694810 2.694810 0.2944070 1 \n5 0.6857206 2.865803 2.865803 0.7495994 1 \n6 0.5126451 2.999560 2.999560 1.1543489 1 "},"metadata":{}}]},{"cell_type":"markdown","source":"# # Calculate correlation of the data","metadata":{}},{"cell_type":"code","source":"cor.data<-cor(app_sub[,1:10])\ncor.data","metadata":{"execution":{"iopub.status.busy":"2023-02-25T21:26:19.642126Z","iopub.execute_input":"2023-02-25T21:26:19.644687Z","iopub.status.idle":"2023-02-25T21:26:19.745084Z"},"trusted":true},"execution_count":282,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A matrix: 10 × 10 of type dbl</caption>\n<thead>\n\t<tr><th></th><th scope=col>volume</th><th scope=col>lag1</th><th scope=col>lag2</th><th scope=col>lag3</th><th scope=col>lag4</th><th scope=col>lag5</th><th scope=col>roll_sd</th><th scope=col>roll_mean</th><th scope=col>ma10</th><th scope=col>ma20</th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>volume</th><td> 1.00000000</td><td>-0.06024089</td><td>-0.04608028</td><td>-0.036068053</td><td>-0.034482258</td><td>-0.031586490</td><td>-0.360477319</td><td>-0.510363199</td><td>-0.510363199</td><td>-0.509555820</td></tr>\n\t<tr><th scope=row>lag1</th><td>-0.06024089</td><td> 1.00000000</td><td>-0.02874344</td><td>-0.021520378</td><td>-0.012511723</td><td> 0.010066197</td><td>-0.011014877</td><td>-0.011922173</td><td>-0.011922173</td><td>-0.013813334</td></tr>\n\t<tr><th scope=row>lag2</th><td>-0.04608028</td><td>-0.02874344</td><td> 1.00000000</td><td>-0.029615382</td><td>-0.026975148</td><td>-0.024693697</td><td>-0.008355930</td><td>-0.010942183</td><td>-0.010942183</td><td>-0.013654244</td></tr>\n\t<tr><th scope=row>lag3</th><td>-0.03606805</td><td>-0.02152038</td><td>-0.02961538</td><td> 1.000000000</td><td>-0.025921509</td><td>-0.017942017</td><td>-0.005265841</td><td>-0.009225836</td><td>-0.009225836</td><td>-0.012558305</td></tr>\n\t<tr><th scope=row>lag4</th><td>-0.03448226</td><td>-0.01251172</td><td>-0.02697515</td><td>-0.025921509</td><td> 1.000000000</td><td> 0.023619295</td><td>-0.003968882</td><td>-0.004855945</td><td>-0.004855945</td><td>-0.008726771</td></tr>\n\t<tr><th scope=row>lag5</th><td>-0.03158649</td><td> 0.01006620</td><td>-0.02469370</td><td>-0.017942017</td><td> 0.023619295</td><td> 1.000000000</td><td>-0.007781264</td><td> 0.001564239</td><td> 0.001564239</td><td>-0.002363918</td></tr>\n\t<tr><th scope=row>roll_sd</th><td>-0.36047732</td><td>-0.01101488</td><td>-0.00835593</td><td>-0.005265841</td><td>-0.003968882</td><td>-0.007781264</td><td> 1.000000000</td><td> 0.846898700</td><td> 0.846898700</td><td> 0.849109739</td></tr>\n\t<tr><th scope=row>roll_mean</th><td>-0.51036320</td><td>-0.01192217</td><td>-0.01094218</td><td>-0.009225836</td><td>-0.004855945</td><td> 0.001564239</td><td> 0.846898700</td><td> 1.000000000</td><td> 1.000000000</td><td> 0.999461472</td></tr>\n\t<tr><th scope=row>ma10</th><td>-0.51036320</td><td>-0.01192217</td><td>-0.01094218</td><td>-0.009225836</td><td>-0.004855945</td><td> 0.001564239</td><td> 0.846898700</td><td> 1.000000000</td><td> 1.000000000</td><td> 0.999461472</td></tr>\n\t<tr><th scope=row>ma20</th><td>-0.50955582</td><td>-0.01381333</td><td>-0.01365424</td><td>-0.012558305</td><td>-0.008726771</td><td>-0.002363918</td><td> 0.849109739</td><td> 0.999461472</td><td> 0.999461472</td><td> 1.000000000</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA matrix: 10 × 10 of type dbl\n\n| <!--/--> | volume | lag1 | lag2 | lag3 | lag4 | lag5 | roll_sd | roll_mean | ma10 | ma20 |\n|---|---|---|---|---|---|---|---|---|---|---|\n| volume | 1.00000000 | -0.06024089 | -0.04608028 | -0.036068053 | -0.034482258 | -0.031586490 | -0.360477319 | -0.510363199 | -0.510363199 | -0.509555820 |\n| lag1 | -0.06024089 | 1.00000000 | -0.02874344 | -0.021520378 | -0.012511723 | 0.010066197 | -0.011014877 | -0.011922173 | -0.011922173 | -0.013813334 |\n| lag2 | -0.04608028 | -0.02874344 | 1.00000000 | -0.029615382 | -0.026975148 | -0.024693697 | -0.008355930 | -0.010942183 | -0.010942183 | -0.013654244 |\n| lag3 | -0.03606805 | -0.02152038 | -0.02961538 | 1.000000000 | -0.025921509 | -0.017942017 | -0.005265841 | -0.009225836 | -0.009225836 | -0.012558305 |\n| lag4 | -0.03448226 | -0.01251172 | -0.02697515 | -0.025921509 | 1.000000000 | 0.023619295 | -0.003968882 | -0.004855945 | -0.004855945 | -0.008726771 |\n| lag5 | -0.03158649 | 0.01006620 | -0.02469370 | -0.017942017 | 0.023619295 | 1.000000000 | -0.007781264 | 0.001564239 | 0.001564239 | -0.002363918 |\n| roll_sd | -0.36047732 | -0.01101488 | -0.00835593 | -0.005265841 | -0.003968882 | -0.007781264 | 1.000000000 | 0.846898700 | 0.846898700 | 0.849109739 |\n| roll_mean | -0.51036320 | -0.01192217 | -0.01094218 | -0.009225836 | -0.004855945 | 0.001564239 | 0.846898700 | 1.000000000 | 1.000000000 | 0.999461472 |\n| ma10 | -0.51036320 | -0.01192217 | -0.01094218 | -0.009225836 | -0.004855945 | 0.001564239 | 0.846898700 | 1.000000000 | 1.000000000 | 0.999461472 |\n| ma20 | -0.50955582 | -0.01381333 | -0.01365424 | -0.012558305 | -0.008726771 | -0.002363918 | 0.849109739 | 0.999461472 | 0.999461472 | 1.000000000 |\n\n","text/latex":"A matrix: 10 × 10 of type dbl\n\\begin{tabular}{r|llllllllll}\n & volume & lag1 & lag2 & lag3 & lag4 & lag5 & roll\\_sd & roll\\_mean & ma10 & ma20\\\\\n\\hline\n\tvolume & 1.00000000 & -0.06024089 & -0.04608028 & -0.036068053 & -0.034482258 & -0.031586490 & -0.360477319 & -0.510363199 & -0.510363199 & -0.509555820\\\\\n\tlag1 & -0.06024089 & 1.00000000 & -0.02874344 & -0.021520378 & -0.012511723 & 0.010066197 & -0.011014877 & -0.011922173 & -0.011922173 & -0.013813334\\\\\n\tlag2 & -0.04608028 & -0.02874344 & 1.00000000 & -0.029615382 & -0.026975148 & -0.024693697 & -0.008355930 & -0.010942183 & -0.010942183 & -0.013654244\\\\\n\tlag3 & -0.03606805 & -0.02152038 & -0.02961538 & 1.000000000 & -0.025921509 & -0.017942017 & -0.005265841 & -0.009225836 & -0.009225836 & -0.012558305\\\\\n\tlag4 & -0.03448226 & -0.01251172 & -0.02697515 & -0.025921509 & 1.000000000 & 0.023619295 & -0.003968882 & -0.004855945 & -0.004855945 & -0.008726771\\\\\n\tlag5 & -0.03158649 & 0.01006620 & -0.02469370 & -0.017942017 & 0.023619295 & 1.000000000 & -0.007781264 & 0.001564239 & 0.001564239 & -0.002363918\\\\\n\troll\\_sd & -0.36047732 & -0.01101488 & -0.00835593 & -0.005265841 & -0.003968882 & -0.007781264 & 1.000000000 & 0.846898700 & 0.846898700 & 0.849109739\\\\\n\troll\\_mean & -0.51036320 & -0.01192217 & -0.01094218 & -0.009225836 & -0.004855945 & 0.001564239 & 0.846898700 & 1.000000000 & 1.000000000 & 0.999461472\\\\\n\tma10 & -0.51036320 & -0.01192217 & -0.01094218 & -0.009225836 & -0.004855945 & 0.001564239 & 0.846898700 & 1.000000000 & 1.000000000 & 0.999461472\\\\\n\tma20 & -0.50955582 & -0.01381333 & -0.01365424 & -0.012558305 & -0.008726771 & -0.002363918 & 0.849109739 & 0.999461472 & 0.999461472 & 1.000000000\\\\\n\\end{tabular}\n","text/plain":" volume lag1 lag2 lag3 lag4 \nvolume 1.00000000 -0.06024089 -0.04608028 -0.036068053 -0.034482258\nlag1 -0.06024089 1.00000000 -0.02874344 -0.021520378 -0.012511723\nlag2 -0.04608028 -0.02874344 1.00000000 -0.029615382 -0.026975148\nlag3 -0.03606805 -0.02152038 -0.02961538 1.000000000 -0.025921509\nlag4 -0.03448226 -0.01251172 -0.02697515 -0.025921509 1.000000000\nlag5 -0.03158649 0.01006620 -0.02469370 -0.017942017 0.023619295\nroll_sd -0.36047732 -0.01101488 -0.00835593 -0.005265841 -0.003968882\nroll_mean -0.51036320 -0.01192217 -0.01094218 -0.009225836 -0.004855945\nma10 -0.51036320 -0.01192217 -0.01094218 -0.009225836 -0.004855945\nma20 -0.50955582 -0.01381333 -0.01365424 -0.012558305 -0.008726771\n lag5 roll_sd roll_mean ma10 ma20 \nvolume -0.031586490 -0.360477319 -0.510363199 -0.510363199 -0.509555820\nlag1 0.010066197 -0.011014877 -0.011922173 -0.011922173 -0.013813334\nlag2 -0.024693697 -0.008355930 -0.010942183 -0.010942183 -0.013654244\nlag3 -0.017942017 -0.005265841 -0.009225836 -0.009225836 -0.012558305\nlag4 0.023619295 -0.003968882 -0.004855945 -0.004855945 -0.008726771\nlag5 1.000000000 -0.007781264 0.001564239 0.001564239 -0.002363918\nroll_sd -0.007781264 1.000000000 0.846898700 0.846898700 0.849109739\nroll_mean 0.001564239 0.846898700 1.000000000 1.000000000 0.999461472\nma10 0.001564239 0.846898700 1.000000000 1.000000000 0.999461472\nma20 -0.002363918 0.849109739 0.999461472 0.999461472 1.000000000"},"metadata":{}}]},{"cell_type":"code","source":"options(repr.plot.width=20, repr.plot.height=10)\ncorrplot(cor.data,col = colorRampPalette(c(\"green\", \"blue\",\"yellow\", 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lR8gaduVMyuBmFUfGHgF8zWiiklwaaBHBwRAIDgQIMQAIBqOWOU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\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EBqAAAAb9leGpUj5vb53fynrYtuvO+UB9dntup27WNzbxrVPPChTfNn/+9/31y4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\naTV37gcHDuyru7Nz5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tTdG2M8+5v87Z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mUpOUX3vxtkdzDk/Ot028TibmUks2wlJmnU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\nu5kkFsvSwIGnq0nfvioo8O/k1C8yRn37qv2pX3jZt6/ataNijYxRz54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repr.plot.height=10)\n# Create a correlation plot with colorful cells\ncorrplot(cor.data, method = \"color\", type = \"upper\",\n tl.col = \"black\", tl.srt = 45,\n addCoef.col = \"black\", number.cex = 0.9,\n col = colorRampPalette(c(\"green\", \"blue\",\"yellow\", 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Check the structure of the data","metadata":{}},{"cell_type":"code","source":"#structure of the data\nstr(app_sub)\n","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:05:01.984006Z","iopub.execute_input":"2023-02-25T20:05:01.985539Z","iopub.status.idle":"2023-02-25T20:05:02.008832Z"},"trusted":true},"execution_count":235,"outputs":[{"name":"stdout","text":"'data.frame':\t4065 obs. of 11 variables:\n $ volume : num 1.24e+09 8.47e+08 8.35e+08 7.97e+08 3.35e+09 ...\n $ lag1 : num 0.07325 0.05596 0.02195 -0.00715 0.00493 ...\n $ lag2 : num 0.05218 0.07325 0.05596 0.02195 -0.00715 ...\n $ lag3 : num -0.0289 0.0522 0.0732 0.056 0.022 ...\n $ lag4 : num -0.1915 -0.0289 0.0522 0.0732 0.056 ...\n $ lag5 : num -0.4574 -0.1915 -0.0289 0.0522 0.0732 ...\n $ roll_sd : num 1.966 1.544 1.194 0.911 0.686 ...\n $ roll_mean: num 1.91 2.22 2.48 2.69 2.87 ...\n $ ma10 : num 1.91 2.22 2.48 2.69 2.87 ...\n $ ma20 : num -1.403 -0.779 -0.214 0.294 0.75 ...\n $ Direction: chr \"1\" \"1\" \"0\" \"1\" ...\n","output_type":"stream"}]},{"cell_type":"markdown","source":"****As the direction variable is a character, we will convert it into a factor.","metadata":{}},{"cell_type":"code","source":"###convert charater data into a factor\napp_sub$Direction <- factor(app_sub$Direction)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:05:06.106959Z","iopub.execute_input":"2023-02-25T20:05:06.108486Z","iopub.status.idle":"2023-02-25T20:05:06.121491Z"},"trusted":true},"execution_count":236,"outputs":[]},{"cell_type":"markdown","source":"# Split data into train and test","metadata":{}},{"cell_type":"code","source":"set.seed(101)\nsplit = sample.split(app_sub$Direction, SplitRatio = 0.70)\ntrain = subset(app_sub, split == TRUE)\ntest = subset(app_sub, split == FALSE)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:05:11.426835Z","iopub.execute_input":"2023-02-25T20:05:11.428343Z","iopub.status.idle":"2023-02-25T20:05:11.458457Z"},"trusted":true},"execution_count":237,"outputs":[]},{"cell_type":"code","source":"# Split the data into training and test sets\nsplit = sample.split(app_sub$Direction, SplitRatio = 0.70)\ntrain = subset(app_sub, split == TRUE)\ntest = subset(app_sub, split == FALSE)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:05:13.863665Z","iopub.execute_input":"2023-02-25T20:05:13.865215Z","iopub.status.idle":"2023-02-25T20:05:13.886146Z"},"trusted":true},"execution_count":238,"outputs":[]},{"cell_type":"code","source":"# Create separate dependent and independent variables\ntrain_x <- train[, 1:10] # independent variables\ntrain_y <- train$Direction # dependent variable\n\ntest_x <- test[, 1:10] # independent variables\ntest_y <- test$Direction # dependent variable","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:05:16.875224Z","iopub.execute_input":"2023-02-25T20:05:16.876746Z","iopub.status.idle":"2023-02-25T20:05:16.894795Z"},"trusted":true},"execution_count":239,"outputs":[]},{"cell_type":"code","source":"head(train_x)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:05:35.593703Z","iopub.execute_input":"2023-02-25T20:05:35.595322Z","iopub.status.idle":"2023-02-25T20:05:35.623703Z"},"trusted":true},"execution_count":241,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 10</caption>\n<thead>\n\t<tr><th></th><th scope=col>volume</th><th scope=col>lag1</th><th scope=col>lag2</th><th scope=col>lag3</th><th scope=col>lag4</th><th scope=col>lag5</th><th scope=col>roll_sd</th><th scope=col>roll_mean</th><th scope=col>ma10</th><th scope=col>ma20</th></tr>\n\t<tr><th></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>1238319600</td><td> 0.073245269</td><td> 0.052181885</td><td>-0.028858272</td><td>-0.19150305</td><td>-0.457380295</td><td>1.9662026</td><td>1.910904</td><td>1.910904</td><td>-1.4032928</td></tr>\n\t<tr><th scope=row>4</th><td> 797106800</td><td>-0.007146747</td><td> 0.021953106</td><td> 0.055959727</td><td> 0.07324527</td><td> 0.052181885</td><td>0.9105575</td><td>2.694810</td><td>2.694810</td><td> 0.2944070</td></tr>\n\t<tr><th scope=row>5</th><td>3349298400</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.021953106</td><td> 0.05595973</td><td> 0.073245269</td><td>0.6857206</td><td>2.865803</td><td>2.865803</td><td> 0.7495994</td></tr>\n\t<tr><th scope=row>6</th><td>2952880000</td><td> 0.079799548</td><td> 0.004926118</td><td>-0.007146747</td><td> 0.02195311</td><td> 0.055959727</td><td>0.5126451</td><td>2.999560</td><td>2.999560</td><td> 1.1543489</td></tr>\n\t<tr><th scope=row>9</th><td>1244076400</td><td>-0.012393855</td><td>-0.012448251</td><td> 0.046746076</td><td> 0.07979955</td><td> 0.004926118</td><td>0.2334215</td><td>3.224906</td><td>3.224906</td><td> 2.0954038</td></tr>\n\t<tr><th scope=row>10</th><td>1646260000</td><td> 0.025872379</td><td>-0.012393855</td><td>-0.012448251</td><td> 0.04674608</td><td> 0.079799548</td><td>0.1968260</td><td>3.257214</td><td>3.257214</td><td> 2.3278458</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 10\n\n| <!--/--> | volume <dbl> | lag1 <dbl> | lag2 <dbl> | lag3 <dbl> | lag4 <dbl> | lag5 <dbl> | roll_sd <dbl> | roll_mean <dbl> | ma10 <dbl> | ma20 <dbl> |\n|---|---|---|---|---|---|---|---|---|---|---|\n| 1 | 1238319600 | 0.073245269 | 0.052181885 | -0.028858272 | -0.19150305 | -0.457380295 | 1.9662026 | 1.910904 | 1.910904 | -1.4032928 |\n| 4 | 797106800 | -0.007146747 | 0.021953106 | 0.055959727 | 0.07324527 | 0.052181885 | 0.9105575 | 2.694810 | 2.694810 | 0.2944070 |\n| 5 | 3349298400 | 0.004926118 | -0.007146747 | 0.021953106 | 0.05595973 | 0.073245269 | 0.6857206 | 2.865803 | 2.865803 | 0.7495994 |\n| 6 | 2952880000 | 0.079799548 | 0.004926118 | -0.007146747 | 0.02195311 | 0.055959727 | 0.5126451 | 2.999560 | 2.999560 | 1.1543489 |\n| 9 | 1244076400 | -0.012393855 | -0.012448251 | 0.046746076 | 0.07979955 | 0.004926118 | 0.2334215 | 3.224906 | 3.224906 | 2.0954038 |\n| 10 | 1646260000 | 0.025872379 | -0.012393855 | -0.012448251 | 0.04674608 | 0.079799548 | 0.1968260 | 3.257214 | 3.257214 | 2.3278458 |\n\n","text/latex":"A data.frame: 6 × 10\n\\begin{tabular}{r|llllllllll}\n & volume & lag1 & lag2 & lag3 & lag4 & lag5 & roll\\_sd & roll\\_mean & ma10 & ma20\\\\\n & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t1 & 1238319600 & 0.073245269 & 0.052181885 & -0.028858272 & -0.19150305 & -0.457380295 & 1.9662026 & 1.910904 & 1.910904 & -1.4032928\\\\\n\t4 & 797106800 & -0.007146747 & 0.021953106 & 0.055959727 & 0.07324527 & 0.052181885 & 0.9105575 & 2.694810 & 2.694810 & 0.2944070\\\\\n\t5 & 3349298400 & 0.004926118 & -0.007146747 & 0.021953106 & 0.05595973 & 0.073245269 & 0.6857206 & 2.865803 & 2.865803 & 0.7495994\\\\\n\t6 & 2952880000 & 0.079799548 & 0.004926118 & -0.007146747 & 0.02195311 & 0.055959727 & 0.5126451 & 2.999560 & 2.999560 & 1.1543489\\\\\n\t9 & 1244076400 & -0.012393855 & -0.012448251 & 0.046746076 & 0.07979955 & 0.004926118 & 0.2334215 & 3.224906 & 3.224906 & 2.0954038\\\\\n\t10 & 1646260000 & 0.025872379 & -0.012393855 & -0.012448251 & 0.04674608 & 0.079799548 & 0.1968260 & 3.257214 & 3.257214 & 2.3278458\\\\\n\\end{tabular}\n","text/plain":" volume lag1 lag2 lag3 lag4 lag5 \n1 1238319600 0.073245269 0.052181885 -0.028858272 -0.19150305 -0.457380295\n4 797106800 -0.007146747 0.021953106 0.055959727 0.07324527 0.052181885\n5 3349298400 0.004926118 -0.007146747 0.021953106 0.05595973 0.073245269\n6 2952880000 0.079799548 0.004926118 -0.007146747 0.02195311 0.055959727\n9 1244076400 -0.012393855 -0.012448251 0.046746076 0.07979955 0.004926118\n10 1646260000 0.025872379 -0.012393855 -0.012448251 0.04674608 0.079799548\n roll_sd roll_mean ma10 ma20 \n1 1.9662026 1.910904 1.910904 -1.4032928\n4 0.9105575 2.694810 2.694810 0.2944070\n5 0.6857206 2.865803 2.865803 0.7495994\n6 0.5126451 2.999560 2.999560 1.1543489\n9 0.2334215 3.224906 3.224906 2.0954038\n10 0.1968260 3.257214 3.257214 2.3278458"},"metadata":{}}]},{"cell_type":"markdown","source":"# Logestic Regression","metadata":{}},{"cell_type":"code","source":"###estimating logistic regression with all independent variables\nglm.fit <- glm(train_y ~lag1+lag2+lag3+lag4+lag5+volume+roll_sd+roll_mean+ma10+ma20, data = train_x,maxit = 1000, family = \"binomial\")","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:05:41.853426Z","iopub.execute_input":"2023-02-25T20:05:41.855040Z","iopub.status.idle":"2023-02-25T20:05:41.888451Z"},"trusted":true},"execution_count":242,"outputs":[]},{"cell_type":"code","source":"###summary of the estimation\nsummary(glm.fit)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:05:44.419635Z","iopub.execute_input":"2023-02-25T20:05:44.421225Z","iopub.status.idle":"2023-02-25T20:05:44.441341Z"},"trusted":true},"execution_count":243,"outputs":[{"output_type":"display_data","data":{"text/plain":"\nCall:\nglm(formula = train_y ~ lag1 + lag2 + lag3 + lag4 + lag5 + volume + \n roll_sd + roll_mean + ma10 + ma20, family = \"binomial\", data = train_x, \n maxit = 1000)\n\nDeviance Residuals: \n Min 1Q Median 3Q Max \n-1.549 -1.234 1.056 1.115 1.776 \n\nCoefficients: (1 not defined because of singularities)\n Estimate Std. Error z value Pr(>|z|) \n(Intercept) 3.051e-01 8.478e-02 3.598 0.000321 ***\nlag1 -2.518e+00 1.885e+00 -1.336 0.181578 \nlag2 -5.959e-01 1.858e+00 -0.321 0.748401 \nlag3 -8.074e-02 1.836e+00 -0.044 0.964921 \nlag4 1.451e+00 1.817e+00 0.798 0.424652 \nlag5 2.348e+00 1.744e+00 1.346 0.178225 \nvolume -2.954e-10 1.215e-10 -2.431 0.015052 * \nroll_sd 8.138e-02 5.391e-02 1.510 0.131123 \nroll_mean 3.484e-02 2.560e-02 1.361 0.173559 \nma10 NA NA NA NA \nma20 -3.864e-02 2.591e-02 -1.491 0.135977 \n---\nSignif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n\n(Dispersion parameter for binomial family taken to be 1)\n\n Null deviance: 3934.0 on 2844 degrees of freedom\nResidual deviance: 3919.7 on 2835 degrees of freedom\nAIC: 3939.7\n\nNumber of Fisher Scoring iterations: 4\n"},"metadata":{}}]},{"cell_type":"markdown","source":"# Predict the probability that market will go up","metadata":{}},{"cell_type":"code","source":"## Predict market direction using the testing data\n#calculate fitted probabilities\nfitted.probabilities <- predict(glm.fit,newdata=test_x,type='response')\nfitted.results <- ifelse(fitted.probabilities > 0.5,1,0)\n# Evaluate the performance of the model\nmisClasificError <- mean(fitted.results != test_y)\nprint(paste('Accuracy',1-misClasificError))","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:05:50.059454Z","iopub.execute_input":"2023-02-25T20:05:50.060964Z","iopub.status.idle":"2023-02-25T20:05:50.098774Z"},"trusted":true},"execution_count":244,"outputs":[{"name":"stderr","text":"Warning message in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :\n“prediction from a rank-deficient fit may be misleading”\n","output_type":"stream"},{"name":"stdout","text":"[1] \"Accuracy 0.536065573770492\"\n","output_type":"stream"}]},{"cell_type":"code","source":"#We can also calculate the confusion matrix\ntable(test_y, fitted.probabilities > 0.5)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:05:53.023828Z","iopub.execute_input":"2023-02-25T20:05:53.025377Z","iopub.status.idle":"2023-02-25T20:05:53.040846Z"},"trusted":true},"execution_count":245,"outputs":[{"output_type":"display_data","data":{"text/plain":" \ntest_y FALSE TRUE\n 0 114 460\n 1 106 540"},"metadata":{}}]},{"cell_type":"markdown","source":"# ROC Curve","metadata":{}},{"cell_type":"code","source":"#set plot figure size\noptions(repr.plot.width=15, repr.plot.height=8)\n# Create ROCR prediction object\npred <- prediction(fitted.probabilities, test_y)\n# Create ROC curve\nperf <- performance(pred, \"tpr\", \"fpr\")\nplot(perf, col = \"blue\", main = \"ROC Curve for glm.fit\")\nabline(a = 0, b = 1, lty = 1, col = \"red\")","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:06:19.364646Z","iopub.execute_input":"2023-02-25T20:06:19.367482Z","iopub.status.idle":"2023-02-25T20:06:19.631390Z"},"trusted":true},"execution_count":247,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAABwgAAAPACAIAAACuBbobAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nL+wTQqu5Gy+lWCRd3HfxyvHM5F1FigoAAIASxN8tAwAA2JbB9f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27ivpMTExMLMN5vNS5cuTU1Nvc6cAwcOSLJYLCUREAAA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\nvvuMjgUAAAAAwG1QjAIA7sqJE1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got this warning message \"glm.fit: fitted probabilities numerically 0 or 1 occurred\" typically occurs when the logistic regression model is overfitting the training data, leading to perfect separation of the outcome variable. This means that the model is able to perfectly predict the outcome variable based on the predictor variables, which is not realistic and can lead to unreliable results when applied to new data.","metadata":{}},{"cell_type":"markdown","source":"There are several ways to address this issue, including simplifying the model by removing some of the predictor variables, using regularization techniques such as Lasso or Ridge regression, or using penalized maximum likelihood estimation methods. It is also important to check the distribution of the outcome variable and ensure that there are no extreme values or outliers that could be influencing the results.","metadata":{}},{"cell_type":"markdown","source":"# Re estimate Logestic Regression with Fewer variables","metadata":{}},{"cell_type":"code","source":"###estimating logistic regression with fewer indicators\nglm.fit <- glm(train_y ~lag1+lag2+lag3+lag4+lag5, data = train_x,maxit = 1000, family = \"binomial\")\n#fitted probabilities\nfitted.probabilities <- predict(glm.fit,newdata=test_x,type='response')\nfitted.results <- ifelse(fitted.probabilities > 0.5,1,0)\nmisClasificError <- mean(fitted.results != test_y)\n#accuracy\nprint(paste('Accuracy',1-misClasificError))\n","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:06:28.512838Z","iopub.execute_input":"2023-02-25T20:06:28.514515Z","iopub.status.idle":"2023-02-25T20:06:28.623323Z"},"trusted":true},"execution_count":248,"outputs":[{"name":"stdout","text":"[1] \"Accuracy 0.532786885245902\"\n","output_type":"stream"}]},{"cell_type":"code","source":"options(repr.plot.width=15, repr.plot.height=8)\n# Create ROCR prediction object\npred <- prediction(fitted.probabilities, test_y)\n# Create ROC curve\nperf <- performance(pred, \"tpr\", \"fpr\")\nplot(perf, col = \"blue\", main = \"ROC Curve for glm.fit\")\nabline(a = 0, b = 1, lty = 1, col = 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+zRnjhYsUGqqGjfW5MkaPlyVK5fAlQDADipaMWqxZCQk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\nVZs2jtsAAAAAAABjUIwCgLv69l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remove unimportant variables","metadata":{}},{"cell_type":"markdown","source":"To remove unimportant variables from your logistic regression model, you can use various model selection techniques, such as stepwise selection, LASSO, or ridge regression.\n\nHere is an example of how to perform stepwise selection to select the most important variables in your model:","metadata":{}},{"cell_type":"markdown","source":"# # Stepwise Regression to Identify Important Variables","metadata":{}},{"cell_type":"code","source":"###estimating logistic regression\nglm.fit <- glm(train_y ~lag1+lag2+lag3+lag4+lag5+volume+roll_sd+roll_mean+ma10+ma20, data = train_x,maxit = 1000, family = \"binomial\")\nmodel_step <- step(glm.fit, direction = \"both\")","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:06:49.647594Z","iopub.execute_input":"2023-02-25T20:06:49.649175Z","iopub.status.idle":"2023-02-25T20:06:51.203429Z"},"trusted":true},"execution_count":251,"outputs":[{"name":"stdout","text":"Start: AIC=3939.73\ntrain_y ~ lag1 + lag2 + lag3 + lag4 + lag5 + volume + roll_sd + \n roll_mean + ma10 + ma20\n\n\nStep: AIC=3939.73\ntrain_y ~ lag1 + lag2 + lag3 + lag4 + lag5 + volume + roll_sd + \n roll_mean + ma20\n\n Df Deviance AIC\n- lag3 1 3919.7 3937.7\n- lag2 1 3919.8 3937.8\n- lag4 1 3920.4 3938.4\n- lag1 1 3921.5 3939.5\n- lag5 1 3921.6 3939.6\n- roll_mean 1 3921.6 3939.6\n<none> 3919.7 3939.7\n- ma20 1 3922.0 3940.0\n- roll_sd 1 3922.0 3940.0\n- volume 1 3925.7 3943.7\n\nStep: AIC=3937.73\ntrain_y ~ lag1 + lag2 + lag4 + lag5 + volume + roll_sd + roll_mean + \n ma20\n\n Df Deviance AIC\n- lag2 1 3919.8 3935.8\n- lag4 1 3920.4 3936.4\n- lag1 1 3921.5 3937.5\n- lag5 1 3921.6 3937.6\n- roll_mean 1 3921.6 3937.6\n<none> 3919.7 3937.7\n- ma20 1 3922.0 3938.0\n- roll_sd 1 3922.0 3938.0\n+ lag3 1 3919.7 3939.7\n- volume 1 3925.7 3941.7\n\nStep: AIC=3935.84\ntrain_y ~ lag1 + lag4 + lag5 + volume + roll_sd + roll_mean + \n ma20\n\n Df Deviance AIC\n- lag4 1 3920.5 3934.5\n- lag1 1 3921.6 3935.6\n- roll_mean 1 3921.6 3935.6\n- lag5 1 3921.7 3935.7\n<none> 3919.8 3935.8\n- ma20 1 3922.0 3936.0\n- roll_sd 1 3922.1 3936.1\n+ lag2 1 3919.7 3937.7\n+ lag3 1 3919.8 3937.8\n- volume 1 3925.7 3939.7\n\nStep: AIC=3934.5\ntrain_y ~ lag1 + lag5 + volume + roll_sd + roll_mean + ma20\n\n Df Deviance AIC\n- lag1 1 3922.3 3934.3\n- lag5 1 3922.4 3934.4\n<none> 3920.5 3934.5\n- roll_mean 1 3922.6 3934.6\n- roll_sd 1 3922.8 3934.8\n- ma20 1 3923.0 3935.0\n+ lag4 1 3919.8 3935.8\n+ lag2 1 3920.4 3936.4\n+ lag3 1 3920.5 3936.5\n- volume 1 3926.6 3938.6\n\nStep: AIC=3934.28\ntrain_y ~ lag5 + volume + roll_sd + roll_mean + ma20\n\n Df Deviance AIC\n- roll_mean 1 3924.1 3934.1\n- lag5 1 3924.2 3934.2\n<none> 3922.3 3934.3\n- ma20 1 3924.5 3934.5\n+ lag1 1 3920.5 3934.5\n- roll_sd 1 3924.6 3934.6\n+ lag4 1 3921.6 3935.6\n+ lag2 1 3922.2 3936.2\n+ lag3 1 3922.3 3936.3\n- volume 1 3928.0 3938.0\n\nStep: AIC=3934.11\ntrain_y ~ lag5 + volume + roll_sd + ma20\n\n Df Deviance AIC\n- roll_sd 1 3926.0 3934.0\n<none> 3924.1 3934.1\n+ roll_mean 1 3922.3 3934.3\n+ ma10 1 3922.3 3934.3\n- lag5 1 3926.6 3934.6\n+ lag1 1 3922.6 3934.6\n+ lag4 1 3923.2 3935.2\n+ lag2 1 3924.1 3936.1\n+ lag3 1 3924.1 3936.1\n- ma20 1 3928.4 3936.4\n- volume 1 3929.9 3937.9\n\nStep: AIC=3933.97\ntrain_y ~ lag5 + volume + ma20\n\n Df Deviance AIC\n<none> 3926.0 3934.0\n+ roll_sd 1 3924.1 3934.1\n- lag5 1 3928.4 3934.4\n+ lag1 1 3924.4 3934.4\n+ roll_mean 1 3924.6 3934.6\n+ ma10 1 3924.6 3934.6\n- ma20 1 3928.8 3934.8\n+ lag4 1 3925.0 3935.0\n+ lag2 1 3926.0 3936.0\n+ lag3 1 3926.0 3936.0\n- volume 1 3930.9 3936.9\n","output_type":"stream"}]},{"cell_type":"code","source":"# Print the summary of the selected model\nsummary(model_step)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:06:59.549585Z","iopub.execute_input":"2023-02-25T20:06:59.551055Z","iopub.status.idle":"2023-02-25T20:06:59.569453Z"},"trusted":true},"execution_count":252,"outputs":[{"output_type":"display_data","data":{"text/plain":"\nCall:\nglm(formula = train_y ~ lag5 + volume + ma20, family = \"binomial\", \n data = train_x, maxit = 1000)\n\nDeviance Residuals: \n Min 1Q Median 3Q Max \n-1.337 -1.234 1.080 1.118 1.732 \n\nCoefficients:\n Estimate Std. Error z value Pr(>|z|) \n(Intercept) 2.810e-01 8.239e-02 3.411 0.000648 ***\nlag5 2.635e+00 1.718e+00 1.534 0.125103 \nvolume -2.631e-10 1.186e-10 -2.218 0.026572 * \nma20 -1.556e-03 9.325e-04 -1.668 0.095297 . \n---\nSignif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n\n(Dispersion parameter for binomial family taken to be 1)\n\n Null deviance: 3934 on 2844 degrees of freedom\nResidual deviance: 3926 on 2841 degrees of freedom\nAIC: 3934\n\nNumber of Fisher Scoring iterations: 3\n"},"metadata":{}}]},{"cell_type":"code","source":"###estimating logistic regression\nglm.fit <- glm(train_y ~lag5+roll_mean+volume, data = train_x,maxit = 1000, family = \"binomial\")\n#fitted probabilities\nfitted.probabilities <- predict(glm.fit,newdata=test_x,type='response')\nfitted.results <- ifelse(fitted.probabilities > 0.5,1,0)\nmisClasificError <- mean(fitted.results != test_y)\n#accuracy\nprint(paste('Accuracy',1-misClasificError))","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:07:05.890244Z","iopub.execute_input":"2023-02-25T20:07:05.891782Z","iopub.status.idle":"2023-02-25T20:07:05.944398Z"},"trusted":true},"execution_count":253,"outputs":[{"name":"stdout","text":"[1] \"Accuracy 0.535245901639344\"\n","output_type":"stream"}]},{"cell_type":"markdown","source":"# Lasso to Identify Important variables","metadata":{}},{"cell_type":"code","source":"library(glmnet)\nx <- train_x\ny <- train_y\n","metadata":{"execution":{"iopub.status.busy":"2023-02-25T22:10:07.837747Z","iopub.execute_input":"2023-02-25T22:10:07.839284Z","iopub.status.idle":"2023-02-25T22:10:07.857776Z"},"trusted":true},"execution_count":284,"outputs":[]},{"cell_type":"code","source":"# Fit a Lasso logistic regression model\nfit <- glmnet(x, y, family = \"binomial\", alpha = 1)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:07:26.475680Z","iopub.execute_input":"2023-02-25T20:07:26.477207Z","iopub.status.idle":"2023-02-25T20:07:26.505020Z"},"trusted":true},"execution_count":255,"outputs":[]},{"cell_type":"code","source":"# Plot the coefficients path\noptions(repr.plot.width=15, repr.plot.height=8)\nplot(fit, xvar = \"lambda\", label = TRUE)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:07:32.722405Z","iopub.execute_input":"2023-02-25T20:07:32.727601Z","iopub.status.idle":"2023-02-25T20:07:32.981371Z"},"trusted":true},"execution_count":256,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAABwgAAAPACAIAAACuBbobAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nemmrxwIAAAAAAAC0jYceeuiWW26ZmNV+Io4JAAAAAAAAAE4owigAA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kruqX0nmSpbhVuXWv2OMdU0plpWv2POdsyTbKmxKh8AAABAeyCM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\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geW1AaeqLOfmldw9SjrjNxMVwdgSMum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\nRMpOpa1k2kqZjtn0OXXFX0iZJZ5ut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O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\nACg5glEAAAAAoOQIRgEAAACAkiMYBQAAAABKjmAUAAAAACg5g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qDh2Ff+4MaTc9mB625bObDxi9/aODD95M8UUtEgCCLRynf/xwPzynaa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\nSUVORK5CYII="},"metadata":{"image/png":{"width":900,"height":480}}}]},{"cell_type":"markdown","source":"# Linear Discrimination Ananlysis","metadata":{}},{"cell_type":"code","source":"library(MASS)\n\nlda.fit=lda(train_y~lag1+lag2+lag3+lag4+lag5+volume+roll_sd+roll_mean+ma10+ma20 ,data = train_x)\nlda.fit","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:10:58.708767Z","iopub.execute_input":"2023-02-25T20:10:58.714553Z","iopub.status.idle":"2023-02-25T20:10:58.819745Z"},"trusted":true},"execution_count":266,"outputs":[{"name":"stderr","text":"Warning message in lda.default(x, grouping, ...):\n“variables are collinear”\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"Call:\nlda(train_y ~ lag1 + lag2 + lag3 + lag4 + lag5 + volume + roll_sd + \n roll_mean + ma10 + ma20, data = train_x)\n\nPrior probabilities of groups:\n 0 1 \n0.4702988 0.5297012 \n\nGroup means:\n lag1 lag2 lag3 lag4 lag5 volume\n0 0.0013440285 0.001257345 0.0006044032 0.0006374857 0.0002564624 381295555\n1 0.0005621052 0.001221511 0.0008025776 0.0015467615 0.0016276496 358651487\n roll_sd roll_mean ma10 ma20\n0 0.9857675 44.05462 44.05462 43.90596\n1 0.9843700 42.99999 42.99999 42.77076\n\nCoefficients of linear discriminants:\n LD1\nlag1 -1.765172e+01\nlag2 -4.180758e+00\nlag3 -6.067496e-01\nlag4 1.002921e+01\nlag5 1.611753e+01\nvolume -2.081936e-09\nroll_sd 5.709104e-01\nroll_mean 1.235455e-01\nma10 1.235455e-01\nma20 -2.738454e-01"},"metadata":{}}]},{"cell_type":"code","source":"# Predict the classes of the testing data using the LDA model\npredictions2 <- predict(lda.fit, newdata = test)$class\n# Convert the market direction to a factor variable with the same levels as predictions\ntest$Direction <- as.factor(test$Direction)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:11:08.785686Z","iopub.execute_input":"2023-02-25T20:11:08.787273Z","iopub.status.idle":"2023-02-25T20:11:08.818904Z"},"trusted":true},"execution_count":267,"outputs":[]},{"cell_type":"code","source":"# Check for missing values in the predictions and Direction variables\nif (any(is.na(predictions2)) || any(is.na(test$Direction2))) {\n stop(\"Missing values in predictions or Direction variable\")\n}","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:11:11.610990Z","iopub.execute_input":"2023-02-25T20:11:11.612612Z","iopub.status.idle":"2023-02-25T20:11:11.625891Z"},"trusted":true},"execution_count":268,"outputs":[]},{"cell_type":"code","source":"# Calculate the accuracy of the LDA model\naccuracy <- mean(predictions2 == test$Direction)\nprint(paste('Accuracy:', accuracy))","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:11:17.033423Z","iopub.execute_input":"2023-02-25T20:11:17.034913Z","iopub.status.idle":"2023-02-25T20:11:17.051205Z"},"trusted":true},"execution_count":269,"outputs":[{"name":"stdout","text":"[1] \"Accuracy: 0.536885245901639\"\n","output_type":"stream"}]},{"cell_type":"code","source":"# Create a confusion matrix\nconfusion_matrix <- table(predictions2, test$Direction)\nconfusion_matrix","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:11:28.272799Z","iopub.execute_input":"2023-02-25T20:11:28.274333Z","iopub.status.idle":"2023-02-25T20:11:28.292695Z"},"trusted":true},"execution_count":270,"outputs":[{"output_type":"display_data","data":{"text/plain":" \npredictions2 0 1\n 0 114 105\n 1 460 541"},"metadata":{}}]},{"cell_type":"code","source":"# Calculate the accuracy\naccuracy <- sum(diag(confusion_matrix)) / sum(confusion_matrix)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:11:35.551569Z","iopub.execute_input":"2023-02-25T20:11:35.553199Z","iopub.status.idle":"2023-02-25T20:11:35.567160Z"},"trusted":true},"execution_count":271,"outputs":[]},{"cell_type":"code","source":"# Print the accuracy\nprint(paste('Accuracy:', accuracy))","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:11:40.157595Z","iopub.execute_input":"2023-02-25T20:11:40.159209Z","iopub.status.idle":"2023-02-25T20:11:40.173794Z"},"trusted":true},"execution_count":272,"outputs":[{"name":"stdout","text":"[1] \"Accuracy: 0.536885245901639\"\n","output_type":"stream"}]},{"cell_type":"markdown","source":"# Quadratic Discrimination Analysis","metadata":{}},{"cell_type":"code","source":"qda.fit <- qda(formula=train_y ~ lag1+lag2+lag3+lag4+lag5,\ndata = train_x)\nqda.fit\n#reduce model\n\nqda.fit\n####fitted probabilities\nfitted.prob <- predict(qda.fit,newdata=test)$class\n###confusion matric\nconfusion_matrix<-table(fitted.prob,test$Direction)\n# Calculate the accuracy\naccuracy <- sum(diag(confusion_matrix)) / sum(confusion_matrix)\n# Print the accuracy\nprint(paste('Accuracy:', accuracy))","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:13:54.980608Z","iopub.execute_input":"2023-02-25T20:13:54.982143Z","iopub.status.idle":"2023-02-25T20:13:55.052606Z"},"trusted":true},"execution_count":274,"outputs":[{"output_type":"display_data","data":{"text/plain":"Call:\nqda(train_y ~ lag1 + lag2 + lag3 + lag4 + lag5, data = train_x)\n\nPrior probabilities of groups:\n 0 1 \n0.4702988 0.5297012 \n\nGroup means:\n lag1 lag2 lag3 lag4 lag5\n0 0.0013440285 0.001257345 0.0006044032 0.0006374857 0.0002564624\n1 0.0005621052 0.001221511 0.0008025776 0.0015467615 0.0016276496"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"Call:\nqda(train_y ~ lag1 + lag2 + lag3 + lag4 + lag5, data = train_x)\n\nPrior probabilities of groups:\n 0 1 \n0.4702988 0.5297012 \n\nGroup means:\n lag1 lag2 lag3 lag4 lag5\n0 0.0013440285 0.001257345 0.0006044032 0.0006374857 0.0002564624\n1 0.0005621052 0.001221511 0.0008025776 0.0015467615 0.0016276496"},"metadata":{}},{"name":"stdout","text":"[1] \"Accuracy: 0.527049180327869\"\n","output_type":"stream"}]},{"cell_type":"code","source":"confusion_matrix","metadata":{"execution":{"iopub.status.busy":"2023-02-25T20:14:11.012508Z","iopub.execute_input":"2023-02-25T20:14:11.014038Z","iopub.status.idle":"2023-02-25T20:14:11.029324Z"},"trusted":true},"execution_count":275,"outputs":[{"output_type":"display_data","data":{"text/plain":" \nfitted.prob 0 1\n 0 156 159\n 1 418 487"},"metadata":{}}]},{"cell_type":"markdown","source":"# Combine ROC Curve","metadata":{}},{"cell_type":"code","source":"#Combine ROC curve for all fitted models\n#set the tite andaxis size\noptions(repr.plot.width=20, repr.plot.height=10)\n# Set the font size\npar(cex.main = 2, cex.axis = 1.5, cex.lab = 1.5)\nroc.curve(test_y,fitted.probabilities,main=\"Combile ROC curve for LR,LDA and QDA\",col=1, \n lwd=2, lty=1)\nroc.curve(test_y,predictions2, add=TRUE, col=2, \n lwd=2, lty=2)\nroc.curve(test_y,fitted.prob, add=TRUE, col=3, \n lwd=2, lty=3)\n\nlegend(\"bottomright\", c(\"Logestic Regression\", \"linear discrimination analysis\", \"Qudartic Discrimination Analysis\"), \n col=1:6, lty=1:6, lwd=2)","metadata":{"execution":{"iopub.status.busy":"2023-02-25T22:42:32.488889Z","iopub.execute_input":"2023-02-25T22:42:32.494083Z","iopub.status.idle":"2023-02-25T22:42:32.776346Z"},"trusted":true},"execution_count":308,"outputs":[{"output_type":"display_data","data":{"text/plain":"Area under the curve (AUC): 0.527"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"Area under the curve (AUC): 0.518"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"Area under the curve (AUC): 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UulysYDBqNRkVRFEWxWtvVEwAA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\nAeHtHz355Bmz9z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