forecasting-time-series-data-with-prophet-i-&-ii.nextjournal.ipynb

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:exec-duration 181}}","runtime-id":"8468502d-75f0-4cea-8eb8-5fd901cd4a0f","url":"https:\/\/staging.nextjournal.com\/eric-brown\/forecasting-with-prophet"}},"cells":[{"cell_type":"markdown","metadata":{},"source":["# Forecasting Time Series Data With Prophet I & II\n\n<h2 class=\"pm-node nj-subtitle\">Parts 1 and 2 of 4<\/h2>\n\n<p class=\"pm-node nj-authors\">Eric D. Brown, D.Sc.<\/p>\n\nOriginally published as *[Forecasting Time-Series data with Prophet](https:\/\/pythondata.com\/forecasting-time-series-data-with-prophet-part-1\/)* at [pythondata.com](https:\/\/pythondata.com\/).\n\n# Introduction\n\nA lot of what I do in [my data analytics work](https:\/\/pythondata.com\/hire-me\/) is understanding time series data, modeling that data and trying to forecast what might come next in that data. Over the years I\u2019ve used many different approaches, libraries, and modeling techniques for modeling and forecasting with some success\u2026 and a lot of failure.\n\nRecently, I\u2019ve been looking for a simpler approach for my initial modeling and think I\u2019ve found a very nice library in [Facebook\u2019s Prophet](https:\/\/facebookincubator.github.io\/prophet\/) (available for both Python and R). While this particular library isn\u2019t terribly robust, it is quick and gives some very good results for that initial pass at modeling \/ forecasting time series data. An added bonus with Prophet for those that like to understand the theory behind things is [this white paper](https:\/\/facebookincubator.github.io\/prophet\/static\/prophet_paper_20170113.pdf) with a very good description of the math \/ statistical approach behind Prophet.\n\nIf you are interested in learning more about time-series forecasting, check out the books \/ websites below.\n\n* [Introduction to Time Series and Forecasting](http:\/\/amzn.to\/2rY3Wrg)\n* [Modeling Techniques in Predictive Analytics with Python and R: A Guide to Data Science](http:\/\/amzn.to\/2qEgqA7)\n* [Forecasting: principles and practice](https:\/\/www.otexts.org\/book\/fpp)\n* [Time-Critical Decision Making for Business Administration](http:\/\/home.ubalt.edu\/ntsbarsh\/stat-data\/Forecast.htm)\n\n# Part I\n\n## Getting Started\n\nUsing Prophet is extremely straightforward. You import it, load some data into a Pandas dataframe, set the data up into the proper format and then start modeling \/ forecasting.\n\nFirst, import the module (plus some other modules that we\u2019ll need):"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"1d08162b-1f73-410b-8086-c100dcd1ee6e","kind":"code","language":"python"}},"source":["import pandas as pd\nimport numpy as np\nfrom fbprophet import Prophet\nimport matplotlib.pyplot as plt\n \nplt.rcParams['figure.figsize']=(20,10)\nplt.style.use('ggplot')"],"outputs":[],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Matplotlib must be manually registered with Pandas due to [a conflict between Prophet and Pandas](https:\/\/nextjournal.com\/blog\/facebook-prophet\/)."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"47e6ae8e-dd52-40e4-8a89-b77cac42c6b3","kind":"code","language":"python"}},"source":["pd.plotting.register_matplotlib_converters()"],"outputs":[],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["## Read in the data\n\n[retail_sales.csv](https:\/\/staging.nextjournal.com\/data\/QmfNEyUeCcw8tEkoYTJTTtRSMy6E9HUTDHvy9cgsZRTTsM?content-type=text\/csv&node-id=c6624fe3-ee14-44a4-9401-9cf6609388b8&filename=retail_sales.csv&node-kind=file)\n\nRead the data in from the `retail_sales.csv` file and set the index to the `date` column. We are also parsing dates in the data file."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"6401ddbc-c5b4-4f59-bbb3-0c6cfdb0298d","kind":"code","language":"python"}},"source":["sales_df = pd.read_csv(","\"\/.nextjournal\/data-named\/QmfNEyUeCcw8tEkoYTJTTtRSMy6E9HUTDHvy9cgsZRTTsM\/retail_sales.csv\"",", index_col='date', parse_dates=True)"],"outputs":[],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Now, we have a Pandas dataframe with our data that looks something like this:"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"e05362a3-3c6a-4adc-beb5-bb45b6d0c470","kind":"code","language":"python"}},"source":["sales_df.head()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"             ...-02-01  311022","text\/csv":"date,sales\n2009-10-01,338630\n2009-11-01,339386\n2009-12-01,400264\n2010-01-01,314640\n2010-02-01,311022\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th><\/th>\n      <th>sales<\/th>\n    <\/tr>\n    <tr>\n      <th>date<\/th>\n      <th><\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <th>2009-10-01<\/th>\n      <td>338630<\/td>\n    <\/tr>\n    <tr>\n      <th>2009-11-01<\/th>\n      <td>339386<\/td>\n    <\/tr>\n    <tr>\n      <th>2009-12-01<\/th>\n      <td>400264<\/td>\n    <\/tr>\n    <tr>\n      <th>2010-01-01<\/th>\n      <td>314640<\/td>\n    <\/tr>\n    <tr>\n      <th>2010-02-01<\/th>\n      <td>311022<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["## Prepare for Prophet\n\nFor Prophet to work, we need to change the names of these columns to `ds` and `y`, so lets just create a new dataframe and keep our old one handy (you'll see why later). The new dataframe will initially be created with an integer index so we can rename the columns"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"034b4ee6-1b97-4b56-8719-e6ff8278c2b4","kind":"code","language":"python"}},"source":["df = sales_df.reset_index()"],"outputs":[],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Your dataframe should now look like the following:"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"4d4ac40d-800b-4fab-b3bc-44927e66b195","kind":"code","language":"python"}},"source":["df.head()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"        date ...-02-01  311022","text\/csv":",date,sales\n0,2009-10-01,338630\n1,2009-11-01,339386\n2,2009-12-01,400264\n3,2010-01-01,314640\n4,2010-02-01,311022\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th><\/th>\n      <th>date<\/th>\n      <th>sales<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <th>0<\/th>\n      <td>2009-10-01<\/td>\n      <td>338630<\/td>\n    <\/tr>\n    <tr>\n      <th>1<\/th>\n      <td>2009-11-01<\/td>\n      <td>339386<\/td>\n    <\/tr>\n    <tr>\n      <th>2<\/th>\n      <td>2009-12-01<\/td>\n      <td>400264<\/td>\n    <\/tr>\n    <tr>\n      <th>3<\/th>\n      <td>2010-01-01<\/td>\n      <td>314640<\/td>\n    <\/tr>\n    <tr>\n      <th>4<\/th>\n      <td>2010-02-01<\/td>\n      <td>311022<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Let's rename the columns as required by `fbprophet`. Additionally, `fbprophet` doesn't like the index to be a datetime... it wants to see `ds` as a non-index column, so we won't set an index differently than the integer index."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"4efa9fd5-f0c9-4175-96cd-9de9ea253c42","kind":"code","language":"python"}},"source":["df=df.rename(columns={'date':'ds', 'sales':'y'})"],"outputs":[],"execution_count":1},{"cell_type":"code","metadata":{"nextjournal":{"id":"161acdec-c9df-4772-abbc-8a102f2ab4cc","kind":"code","language":"python"}},"source":["df.head()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"          ds ...-02-01  311022","text\/csv":",ds,y\n0,2009-10-01,338630\n1,2009-11-01,339386\n2,2009-12-01,400264\n3,2010-01-01,314640\n4,2010-02-01,311022\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th><\/th>\n      <th>ds<\/th>\n      <th>y<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <th>0<\/th>\n      <td>2009-10-01<\/td>\n      <td>338630<\/td>\n    <\/tr>\n    <tr>\n      <th>1<\/th>\n      <td>2009-11-01<\/td>\n      <td>339386<\/td>\n    <\/tr>\n    <tr>\n      <th>2<\/th>\n      <td>2009-12-01<\/td>\n      <td>400264<\/td>\n    <\/tr>\n    <tr>\n      <th>3<\/th>\n      <td>2010-01-01<\/td>\n      <td>314640<\/td>\n    <\/tr>\n    <tr>\n      <th>4<\/th>\n      <td>2010-02-01<\/td>\n      <td>311022<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Now's a good time to take a look at your data. Plot the data using Pandas' `plot` function."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"fa9bf8d8-4926-4e89-a945-d0d350ba5662","kind":"code","language":"python"}},"source":["df.set_index('ds').y.plot().get_figure()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"<Figure size ...0 with 1 Axes>","image\/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-\/\/W3C\/\/DTD SVG 1.1\/\/EN\"\n  \"http:\/\/www.w3.org\/Graphics\/SVG\/1.1\/DTD\/svg11.dtd\">\n<!-- Created with matplotlib (https:\/\/matplotlib.org\/) -->\n<svg height=\"720pt\" version=\"1.1\" viewBox=\"0 0 1440 720\" width=\"1440pt\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\">\n <defs>\n  <style type=\"text\/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  <\/style>\n <\/defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 720 \nL 1440 720 \nL 1440 0 \nL 0 0 \nz\n\" 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Facebook Prophet's example uses the log-transform as a way to remove some of these anomalies but it isn't the absolute 'best' way to do this... but given that its the example and a simple data series, I'll follow their lead for now. Taking the log of a number is easily reversible to be able to see your original data.\n\nTo log-transform your data, you can use Numpy's `log()` function"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"5120a351-c126-42fc-b5f9-9f379cab6586","kind":"code","language":"python"}},"source":["df['y'] = np.log(df['y'])"],"outputs":[],"execution_count":1},{"cell_type":"code","metadata":{"nextjournal":{"id":"fc728992-a3de-47ba-9f82-13913ab36ba0","kind":"code","language":"python"}},"source":["df.tail()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"           ds...-01  12.973671","text\/csv":",ds,y\n67,2015-05-01,13.044650453675313\n68,2015-06-01,13.013059541513272\n69,2015-07-01,13.033991074775358\n70,2015-08-01,13.030993424699561\n71,2015-09-01,12.973670775134828\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    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monthly data, you'll see a message from Prophet saying `Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.` This is OK since we are working with monthly data but you can disable it by using `weekly_seasonality=True` in the instantiation of Prophet."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"45b5079c-6745-4493-8671-5f30aecc3a8b","kind":"code","language":"python"}},"source":["model = Prophet()\nmodel.fit(df);"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"<fbprophet.fo...x7f2c11972f60>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Forecasting is fairly useless unless you can look into the future, so we need to add some future dates to our dataframe. For this example, I want to forecast 2 years into the future, so I'll built a future dataframe with 24 periods since we are working with monthly data. Note the `freq='m'` inclusion to ensure we are adding 24 months of data.\n\nThis can be done with the following code:"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"8d70a482-ead6-4156-b424-d3190788af44","kind":"code","language":"python"}},"source":["future = model.make_future_dataframe(periods=24, freq = 'm')\nfuture.tail()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"           ds...\n95 2017-08-31","text\/csv":",ds\n91,2017-04-30\n92,2017-05-31\n93,2017-06-30\n94,2017-07-31\n95,2017-08-31\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th><\/th>\n      <th>ds<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <th>91<\/th>\n      <td>2017-04-30<\/td>\n    <\/tr>\n    <tr>\n      <th>92<\/th>\n      <td>2017-05-31<\/td>\n    <\/tr>\n    <tr>\n      <th>93<\/th>\n      <td>2017-06-30<\/td>\n    <\/tr>\n    <tr>\n      <th>94<\/th>\n      <td>2017-07-31<\/td>\n    <\/tr>\n    <tr>\n      <th>95<\/th>\n      <td>2017-08-31<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["To forecast this future data, we need to run it through Prophet's model."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"49f49fde-0d58-4de9-9b5b-c0a530c12d64","kind":"code","language":"python"}},"source":["forecast = model.predict(future)"],"outputs":[],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["The resulting forecast dataframe contains quite a bit of data, but we really only care about a few columns.  First, let's look at the full dataframe:"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"ffa6eed0-59aa-4d99-913b-135dff1e1cf4","kind":"code","language":"python"}},"source":["forecast.tail()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"           ds... x 16 columns]","text\/csv":",ds,trend,yhat_lower,yhat_upper,trend_lower,trend_upper,additive_terms,additive_terms_lower,additive_terms_upper,yearly,yearly_lower,yearly_upper,multiplicative_terms,multiplicative_terms_lower,multiplicative_terms_upper,yhat\n91,2017-04-30,13.04123652349171,12.869830771361567,13.255463589763021,12.84789227276585,13.23462041108603,0.018364387938210127,0.018364387938210127,0.018364387938210127,0.018364387938210127,0.018364387938210127,0.018364387938210127,0.0,0.0,0.0,13.05960091142992\n92,2017-05-31,13.042941867496479,12.850437269055105,13.270689789903539,12.836270260891151,13.256559935712213,0.01293233813410532,0.01293233813410532,0.01293233813410532,0.01293233813410532,0.01293233813410532,0.01293233813410532,0.0,0.0,0.0,13.055874205630584\n93,2017-06-30,13.044592200404322,12.852533665503888,13.31003696452107,12.823707339902164,13.276044202956838,0.03173298183105626,0.03173298183105626,0.03173298183105626,0.03173298183105626,0.03173298183105626,0.03173298183105626,0.0,0.0,0.0,13.076325182235378\n94,2017-07-31,13.046297544409093,12.821363190627153,13.308538566200477,12.811115469126646,13.297534629931295,0.009755370802204946,0.009755370802204946,0.009755370802204946,0.009755370802204946,0.009755370802204946,0.009755370802204946,0.0,0.0,0.0,13.056052915211298\n95,2017-08-31,13.048002888413862,12.773316565048013,13.292583771318434,12.798429450161176,13.31735550685623,-0.020632578364880236,-0.020632578364880236,-0.020632578364880236,-0.020632578364880236,-0.020632578364880236,-0.020632578364880236,0.0,0.0,0.0,13.027370310048981\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th><\/th>\n      <th>ds<\/th>\n      <th>trend<\/th>\n      <th>yhat_lower<\/th>\n      <th>yhat_upper<\/th>\n      <th>trend_lower<\/th>\n      <th>trend_upper<\/th>\n      <th>additive_terms<\/th>\n      <th>additive_terms_lower<\/th>\n      <th>additive_terms_upper<\/th>\n      <th>yearly<\/th>\n      <th>yearly_lower<\/th>\n      <th>yearly_upper<\/th>\n      <th>multiplicative_terms<\/th>\n      <th>multiplicative_terms_lower<\/th>\n      <th>multiplicative_terms_upper<\/th>\n      <th>yhat<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <th>91<\/th>\n      <td>2017-04-30<\/td>\n      <td>13.041237<\/td>\n      <td>12.869831<\/td>\n      <td>13.255464<\/td>\n      <td>12.847892<\/td>\n      <td>13.234620<\/td>\n      <td>0.018364<\/td>\n      <td>0.018364<\/td>\n      <td>0.018364<\/td>\n      <td>0.018364<\/td>\n      <td>0.018364<\/td>\n      <td>0.018364<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>13.059601<\/td>\n    <\/tr>\n    <tr>\n      <th>92<\/th>\n      <td>2017-05-31<\/td>\n      <td>13.042942<\/td>\n      <td>12.850437<\/td>\n      <td>13.270690<\/td>\n      <td>12.836270<\/td>\n      <td>13.256560<\/td>\n      <td>0.012932<\/td>\n      <td>0.012932<\/td>\n      <td>0.012932<\/td>\n      <td>0.012932<\/td>\n      <td>0.012932<\/td>\n      <td>0.012932<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>13.055874<\/td>\n    <\/tr>\n    <tr>\n      <th>93<\/th>\n      <td>2017-06-30<\/td>\n      <td>13.044592<\/td>\n      <td>12.852534<\/td>\n      <td>13.310037<\/td>\n      <td>12.823707<\/td>\n      <td>13.276044<\/td>\n      <td>0.031733<\/td>\n      <td>0.031733<\/td>\n      <td>0.031733<\/td>\n      <td>0.031733<\/td>\n      <td>0.031733<\/td>\n      <td>0.031733<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>13.076325<\/td>\n    <\/tr>\n    <tr>\n      <th>94<\/th>\n      <td>2017-07-31<\/td>\n      <td>13.046298<\/td>\n      <td>12.821363<\/td>\n      <td>13.308539<\/td>\n      <td>12.811115<\/td>\n      <td>13.297535<\/td>\n      <td>0.009755<\/td>\n      <td>0.009755<\/td>\n      <td>0.009755<\/td>\n      <td>0.009755<\/td>\n      <td>0.009755<\/td>\n      <td>0.009755<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>13.056053<\/td>\n    <\/tr>\n    <tr>\n      <th>95<\/th>\n      <td>2017-08-31<\/td>\n      <td>13.048003<\/td>\n      <td>12.773317<\/td>\n      <td>13.292584<\/td>\n      <td>12.798429<\/td>\n      <td>13.317356<\/td>\n      <td>-0.020633<\/td>\n      <td>-0.020633<\/td>\n      <td>-0.020633<\/td>\n      <td>-0.020633<\/td>\n      <td>-0.020633<\/td>\n      <td>-0.020633<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>13.027370<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["We really only want to look at `yhat`, `yhat_lower`, and `yhat_upper`, so we can do that with:"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"75bf1822-0b44-4fbe-a1bb-708d682f0e50","kind":"code","language":"python"}},"source":["forecast[['ds', 'yhat', 'yhat_lower', 'yhat_upper']].tail()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"           ds...17   13.292584","text\/csv":",ds,yhat,yhat_lower,yhat_upper\n91,2017-04-30,13.05960091142992,12.869830771361567,13.255463589763021\n92,2017-05-31,13.055874205630584,12.850437269055105,13.270689789903539\n93,2017-06-30,13.076325182235378,12.852533665503888,13.31003696452107\n94,2017-07-31,13.056052915211298,12.821363190627153,13.308538566200477\n95,2017-08-31,13.027370310048981,12.773316565048013,13.292583771318434\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th><\/th>\n      <th>ds<\/th>\n      <th>yhat<\/th>\n      <th>yhat_lower<\/th>\n      <th>yhat_upper<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <th>91<\/th>\n      <td>2017-04-30<\/td>\n      <td>13.059601<\/td>\n      <td>12.869831<\/td>\n      <td>13.255464<\/td>\n    <\/tr>\n    <tr>\n      <th>92<\/th>\n      <td>2017-05-31<\/td>\n      <td>13.055874<\/td>\n      <td>12.850437<\/td>\n      <td>13.270690<\/td>\n    <\/tr>\n    <tr>\n      <th>93<\/th>\n      <td>2017-06-30<\/td>\n      <td>13.076325<\/td>\n      <td>12.852534<\/td>\n      <td>13.310037<\/td>\n    <\/tr>\n    <tr>\n      <th>94<\/th>\n      <td>2017-07-31<\/td>\n      <td>13.056053<\/td>\n      <td>12.821363<\/td>\n      <td>13.308539<\/td>\n    <\/tr>\n    <tr>\n      <th>95<\/th>\n      <td>2017-08-31<\/td>\n      <td>13.027370<\/td>\n      <td>12.773317<\/td>\n      <td>13.292584<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["## Plotting Prophet results\n\nProphet has a plotting mechanism called `plot`. This plot functionality draws the original data (black dots), the model (blue line), and the error of the forecast (shaded blue area)."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"04a933ad-2ae5-463d-b476-b2421543455b","kind":"code","language":"python"}},"source":["model.plot(forecast);"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"<Figure size ...0 with 1 Axes>","image\/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-\/\/W3C\/\/DTD SVG 1.1\/\/EN\"\n  \"http:\/\/www.w3.org\/Graphics\/SVG\/1.1\/DTD\/svg11.dtd\">\n<!-- Created with matplotlib (https:\/\/matplotlib.org\/) -->\n<svg height=\"432pt\" version=\"1.1\" viewBox=\"0 0 720 432\" width=\"720pt\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\">\n <defs>\n  <style type=\"text\/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  <\/style>\n <\/defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 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The next section describes how I build my own visualization for Prophet modeling.\n\n## Visualizing Prophet models\n\nIn order to build a useful dataframe to visualize our model versus our original data, we need to combine the output of the Prophet model with our original data set, then we'll build a new chart manually using Pandas and Matplotlib.\n\nFirst, let's set our dataframes to have the same index of `ds`."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"248a3bb7-3d25-4ab7-8c37-f43c2fa14ef6","kind":"code","language":"python"}},"source":["df.set_index('ds', inplace=True)\nforecast.set_index('ds', inplace=True)"],"outputs":[],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Now, we'll combine the original data and our forecast model data."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"9b305dc2-987b-45a5-8301-114968a11a80","kind":"code","language":"python"}},"source":["viz_df = sales_df.join(forecast[['yhat', 'yhat_lower','yhat_upper']], how = 'outer')"],"outputs":[],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["If we look at the `head()`, we see the data has been joined correctly but the scales of our original data (`sales`) and our model (`yhat`) are different. We need to rescale the `yhat` column(s) to get the same scale, so we'll use Numpy's `exp` function to do that."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"80000380-852e-4b7f-a22f-af36bdfb367c","kind":"code","language":"python"}},"source":["viz_df.head()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"             ...36   12.665772","text\/csv":",sales,yhat,yhat_lower,yhat_upper\n2009-10-01,338630.0,12.72891629967664,12.719364524183003,12.73949007973038\n2009-11-01,339386.0,12.749435087873692,12.738762885389015,12.75984775702255\n2009-12-01,400264.0,12.887443656406615,12.87722767484526,12.899177627363834\n2010-01-01,314640.0,12.662469402438917,12.65194081078347,12.67338564231148\n2010-02-01,311022.0,12.655825281055929,12.64563618955632,12.665771587151028\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    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    <th>yhat_upper<\/th>\n      <th>yhat_rescaled<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <th>2009-10-01<\/th>\n      <td>338630.0<\/td>\n      <td>12.728916<\/td>\n      <td>12.719365<\/td>\n      <td>12.739490<\/td>\n      <td>337363.512360<\/td>\n    <\/tr>\n    <tr>\n      <th>2009-11-01<\/th>\n      <td>339386.0<\/td>\n      <td>12.749435<\/td>\n      <td>12.738763<\/td>\n      <td>12.759848<\/td>\n      <td>344357.309561<\/td>\n    <\/tr>\n    <tr>\n      <th>2009-12-01<\/th>\n      <td>400264.0<\/td>\n      <td>12.887444<\/td>\n      <td>12.877228<\/td>\n      <td>12.899178<\/td>\n      <td>395317.159208<\/td>\n    <\/tr>\n    <tr>\n      <th>2010-01-01<\/th>\n      <td>314640.0<\/td>\n      <td>12.662469<\/td>\n      <td>12.651941<\/td>\n      <td>12.673386<\/td>\n      <td>315675.290463<\/td>\n    <\/tr>\n    <tr>\n      <th>2010-02-01<\/th>\n      <td>311022.0<\/td>\n      <td>12.655825<\/td>\n      <td>12.645636<\/td>\n      <td>12.665772<\/td>\n      <td>313584.857750<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Let's take a look at the `sales` and `yhat_rescaled` data together in a chart."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"a4b8e8ef-bd1c-4bb4-abcf-c0f0a7b5e97a","kind":"code","language":"python"}},"source":["viz_df[['sales', 'yhat_rescaled']].plot().get_figure()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"<Figure size ...0 with 1 Axes>","image\/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-\/\/W3C\/\/DTD SVG 1.1\/\/EN\"\n  \"http:\/\/www.w3.org\/Graphics\/SVG\/1.1\/DTD\/svg11.dtd\">\n<!-- Created with matplotlib (https:\/\/matplotlib.org\/) -->\n<svg height=\"720pt\" version=\"1.1\" viewBox=\"0 0 1440 720\" width=\"1440pt\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\">\n <defs>\n  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xlink:href=\"#FiraSans-Regular-115\"\/>\n      <use x=\"390.09993\" xlink:href=\"#FiraSans-Regular-99\"\/>\n      <use x=\"437.899918\" xlink:href=\"#FiraSans-Regular-97\"\/>\n      <use x=\"492.299911\" xlink:href=\"#FiraSans-Regular-108\"\/>\n      <use x=\"521.599899\" xlink:href=\"#FiraSans-Regular-101\"\/>\n      <use x=\"576.099884\" xlink:href=\"#FiraSans-Regular-100\"\/>\n     <\/g>\n    <\/g>\n   <\/g>\n  <\/g>\n <\/g>\n <defs>\n  <clipPath id=\"p07f873b8e7\">\n   <rect height=\"489.6\" width=\"1116\" x=\"180\" y=\"86.4\"\/>\n  <\/clipPath>\n <\/defs>\n<\/svg>\n"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["You can see from the chart that the model (blue) is pretty good when plotted against the actual signal (orange) but I like to make my visualizations a little easier to understand. To build my 'better' visualization, we'll need to go back to our original `sales_df` and `forecast` dataframes.\n\nFirst things first - we need to find the 2nd to last date of the original sales data in `sales_df` in order to ensure the original sales data and model data charts are connected."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"45376a2a-ae7b-4d2f-a6b5-51d6e7314381","kind":"code","language":"python"}},"source":["sales_df.index = pd.to_datetime(sales_df.index) #make sure our index as a datetime object\nconnect_date = sales_df.index[-2] #select the 2nd to last date"],"outputs":[],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Using the `connect_date` we can now grab only the model data that after that date (you'll see why in a minute). To do this, we'll mask the forecast data."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"73fd2627-b924-4fb7-83c8-3f7ac7b54347","kind":"code","language":"python"}},"source":["mask = (forecast.index > connect_date)\npredict_df = forecast.loc[mask]"],"outputs":[],"execution_count":1},{"cell_type":"code","metadata":{"nextjournal":{"id":"9429902f-24b4-4dfa-a06f-346a7a047e9f","kind":"code","language":"python"}},"source":["predict_df.head()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"             ... x 15 columns]","text\/csv":"ds,trend,yhat_lower,yhat_upper,trend_lower,trend_upper,additive_terms,additive_terms_lower,additive_terms_upper,yearly,yearly_lower,yearly_upper,multiplicative_terms,multiplicative_terms_lower,multiplicative_terms_upper,yhat\n2015-09-01,13.007844787656373,12.965747579758135,12.985889401175132,13.007844787656373,13.007844787656373,-0.03177395256516356,-0.03177395256516356,-0.03177395256516356,-0.03177395256516356,-0.03177395256516356,-0.03177395256516356,0.0,0.0,0.0,12.976070835091209\n2015-09-30,13.009440109467288,12.971138940891986,12.991256495204917,13.009076227537742,13.010000598832095,-0.027573184792268817,-0.027573184792268817,-0.027573184792268817,-0.027573184792268817,-0.027573184792268817,-0.027573184792268817,0.0,0.0,0.0,12.98186692467502\n2015-10-31,13.011145453472059,12.991105827534323,13.013905846841498,13.007870401050262,13.014788258513624,-0.008439370503070144,-0.008439370503070144,-0.008439370503070144,-0.008439370503070144,-0.008439370503070144,-0.008439370503070144,0.0,0.0,0.0,13.002706082968988\n2015-11-30,13.0127957863799,13.156983635450628,13.183048182462862,13.004982628927213,13.021804930903603,0.15702474754463652,0.15702474754463652,0.15702474754463652,0.15702474754463652,0.15702474754463652,0.15702474754463652,0.0,0.0,0.0,13.169820533924536\n2015-12-31,13.01450113038467,12.854573137604683,12.888716812052115,13.000563912342683,13.029785260602326,-0.1437012799285344,-0.1437012799285344,-0.1437012799285344,-0.1437012799285344,-0.1437012799285344,-0.1437012799285344,0.0,0.0,0.0,12.870799850456136\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th><\/th>\n      <th>trend<\/th>\n      <th>yhat_lower<\/th>\n      <th>yhat_upper<\/th>\n      <th>trend_lower<\/th>\n      <th>trend_upper<\/th>\n      <th>additive_terms<\/th>\n      <th>additive_terms_lower<\/th>\n      <th>additive_terms_upper<\/th>\n      <th>yearly<\/th>\n      <th>yearly_lower<\/th>\n      <th>yearly_upper<\/th>\n      <th>multiplicative_terms<\/th>\n      <th>multiplicative_terms_lower<\/th>\n      <th>multiplicative_terms_upper<\/th>\n      <th>yhat<\/th>\n    <\/tr>\n    <tr>\n      <th>ds<\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n      <th><\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <th>2015-09-01<\/th>\n      <td>13.007845<\/td>\n      <td>12.965748<\/td>\n      <td>12.985889<\/td>\n      <td>13.007845<\/td>\n      <td>13.007845<\/td>\n      <td>-0.031774<\/td>\n      <td>-0.031774<\/td>\n      <td>-0.031774<\/td>\n      <td>-0.031774<\/td>\n      <td>-0.031774<\/td>\n      <td>-0.031774<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>12.976071<\/td>\n    <\/tr>\n    <tr>\n      <th>2015-09-30<\/th>\n      <td>13.009440<\/td>\n      <td>12.971139<\/td>\n      <td>12.991256<\/td>\n      <td>13.009076<\/td>\n      <td>13.010001<\/td>\n      <td>-0.027573<\/td>\n      <td>-0.027573<\/td>\n      <td>-0.027573<\/td>\n      <td>-0.027573<\/td>\n      <td>-0.027573<\/td>\n      <td>-0.027573<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>12.981867<\/td>\n    <\/tr>\n    <tr>\n      <th>2015-10-31<\/th>\n      <td>13.011145<\/td>\n      <td>12.991106<\/td>\n      <td>13.013906<\/td>\n      <td>13.007870<\/td>\n      <td>13.014788<\/td>\n      <td>-0.008439<\/td>\n      <td>-0.008439<\/td>\n      <td>-0.008439<\/td>\n      <td>-0.008439<\/td>\n      <td>-0.008439<\/td>\n      <td>-0.008439<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>13.002706<\/td>\n    <\/tr>\n    <tr>\n      <th>2015-11-30<\/th>\n      <td>13.012796<\/td>\n      <td>13.156984<\/td>\n      <td>13.183048<\/td>\n      <td>13.004983<\/td>\n      <td>13.021805<\/td>\n      <td>0.157025<\/td>\n      <td>0.157025<\/td>\n      <td>0.157025<\/td>\n      <td>0.157025<\/td>\n      <td>0.157025<\/td>\n      <td>0.157025<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>13.169821<\/td>\n    <\/tr>\n    <tr>\n      <th>2015-12-31<\/th>\n      <td>13.014501<\/td>\n      <td>12.854573<\/td>\n      <td>12.888717<\/td>\n      <td>13.000564<\/td>\n      <td>13.029785<\/td>\n      <td>-0.143701<\/td>\n      <td>-0.143701<\/td>\n      <td>-0.143701<\/td>\n      <td>-0.143701<\/td>\n      <td>-0.143701<\/td>\n      <td>-0.143701<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>0.0<\/td>\n      <td>12.870800<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Now, let's build a dataframe to use in our new visualization. We'll follow the same steps we did before."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"59b8703a-ce78-4a55-9af3-137ca022abf2","kind":"code","language":"python"}},"source":["viz_df = sales_df.join(predict_df[['yhat', 'yhat_lower','yhat_upper']], how = 'outer')\nviz_df['yhat_scaled']=np.exp(viz_df['yhat'])"],"outputs":[],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["Now, if we take a look at the `head()` of `viz_df` we'll see `NaN`s everywhere except for our original data rows."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"12d666e8-15e0-4b26-8165-0d1c5ae9595e","kind":"code","language":"python"}},"source":["viz_df.head()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"             ...N          NaN","text\/csv":",sales,yhat,yhat_lower,yhat_upper,yhat_scaled\n2009-10-01,338630.0,,,,\n2009-11-01,339386.0,,,,\n2009-12-01,400264.0,,,,\n2010-01-01,314640.0,,,,\n2010-02-01,311022.0,,,,\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th><\/th>\n      <th>sales<\/th>\n      <th>yhat<\/th>\n      <th>yhat_lower<\/th>\n      <th>yhat_upper<\/th>\n      <th>yhat_scaled<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <th>2009-10-01<\/th>\n      <td>338630.0<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n    <\/tr>\n    <tr>\n      <th>2009-11-01<\/th>\n      <td>339386.0<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n    <\/tr>\n    <tr>\n      <th>2009-12-01<\/th>\n      <td>400264.0<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n    <\/tr>\n    <tr>\n      <th>2010-01-01<\/th>\n      <td>314640.0<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n    <\/tr>\n    <tr>\n      <th>2010-02-01<\/th>\n      <td>311022.0<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n      <td>NaN<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["If we take a look at the `tail()` of the `viz_df` you'll see we have data for the forecast data and `NaNs` for the original data series."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"e6d3f8a5-f297-4125-9ab1-59c1e271c4d2","kind":"code","language":"python"}},"source":["viz_df.tail()"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"            s... 454689.619425","text\/csv":",sales,yhat,yhat_lower,yhat_upper,yhat_scaled\n2017-04-30,,13.05960091142992,12.869830771361567,13.255463589763021,469583.26560153335\n2017-05-31,,13.055874205630584,12.850437269055105,13.270689789903539,467836.5237404679\n2017-06-30,,13.076325182235378,12.852533665503888,13.31003696452107,477502.74244912295\n2017-07-31,,13.056052915211298,12.821363190627153,13.308538566200477,467920.13808058767\n2017-08-31,,13.027370310048981,12.773316565048013,13.292583771318434,454689.61942474794\n","text\/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th><\/th>\n      <th>sales<\/th>\n      <th>yhat<\/th>\n      <th>yhat_lower<\/th>\n      <th>yhat_upper<\/th>\n      <th>yhat_scaled<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <th>2017-04-30<\/th>\n      <td>NaN<\/td>\n      <td>13.059601<\/td>\n      <td>12.869831<\/td>\n      <td>13.255464<\/td>\n      <td>469583.265602<\/td>\n    <\/tr>\n    <tr>\n      <th>2017-05-31<\/th>\n      <td>NaN<\/td>\n      <td>13.055874<\/td>\n      <td>12.850437<\/td>\n      <td>13.270690<\/td>\n      <td>467836.523740<\/td>\n    <\/tr>\n    <tr>\n      <th>2017-06-30<\/th>\n      <td>NaN<\/td>\n      <td>13.076325<\/td>\n      <td>12.852534<\/td>\n      <td>13.310037<\/td>\n      <td>477502.742449<\/td>\n    <\/tr>\n    <tr>\n      <th>2017-07-31<\/th>\n      <td>NaN<\/td>\n      <td>13.056053<\/td>\n      <td>12.821363<\/td>\n      <td>13.308539<\/td>\n      <td>467920.138081<\/td>\n    <\/tr>\n    <tr>\n      <th>2017-08-31<\/th>\n      <td>NaN<\/td>\n      <td>13.027370<\/td>\n      <td>12.773317<\/td>\n      <td>13.292584<\/td>\n      <td>454689.619425<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["## Time to plot\n\nNow, let's plot everything to get the 'final' visualization of our sales data and forecast with errors."]},{"cell_type":"code","metadata":{"nextjournal":{"id":"9511522f-0756-4d75-aa9d-7813fba17cfc","kind":"code","language":"python"}},"source":["fig, ax1 = plt.subplots()\nax1.plot(viz_df.sales)\nax1.plot(viz_df.yhat_scaled, color='black', linestyle=':')\nax1.fill_between(viz_df.index, np.exp(viz_df['yhat_upper']), np.exp(viz_df['yhat_lower']), alpha=0.5, color='darkgray')\nax1.set_title('Sales (Orange) vs Sales Forecast (Black)')\nax1.set_ylabel('Dollar Sales')\nax1.set_xlabel('Date')\n\nL=ax1.legend() #get the legend\nL.get_texts()[0].set_text('Actual Sales') #change the legend text for 1st plot\nL.get_texts()[1].set_text('Forecasted Sales') #change the legend text for 2nd plot\nfig"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"<Figure size ...0 with 1 Axes>","image\/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-\/\/W3C\/\/DTD SVG 1.1\/\/EN\"\n  \"http:\/\/www.w3.org\/Graphics\/SVG\/1.1\/DTD\/svg11.dtd\">\n<!-- Created with matplotlib (https:\/\/matplotlib.org\/) -->\n<svg height=\"720pt\" version=\"1.1\" viewBox=\"0 0 1440 720\" width=\"1440pt\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\">\n <defs>\n  <style type=\"text\/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  <\/style>\n <\/defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 720 \nL 1440 720 \nL 1440 0 \nL 0 0 \nz\n\" style=\"fill:none;\"\/>\n  <\/g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 180 640.8 \nL 1296 640.8 \nL 1296 86.4 \nL 180 86.4 \nz\n\" style=\"fill:none;\"\/>\n   <\/g>\n   <g id=\"matplotlib.axis_1\">\n    <g 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It is much easier to quickly understand and describe what's happening. The orange line is actual sales data and the black dotted line is the forecast. The gray shaded area is the uncertainty estimation of the forecast."]}]}