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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# **Monte Carlo Simulation for Empirically Derived Stock Price Prediction Intervals**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## **I. Introduction**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note: Please don't start trading securities using this technique. Any investment strategies should be rigorously back-tested prior to use. Paper trading is another option for testing strategies and models. Keep in mind that structural breaks exist and can cause a model that used to work to start performing poorly, resulting in lost money. This article is about pairing two statistical techniques to generate empirical prediction intervals. IT IS NOT INVESTMENT ADVICE!\n",
"\n",
"Most time-series libraries for your preferred programming language will give you point predictions and prediction intervals when forecasting. This is of course very useful for making predictions about the future. But what if you want to know the probability that a future value is above some important threshold? An example would be that a stock price in the future is above or below the strike price of an option. That's were pairing Monte Carlo simulation and time series modeling can come in handy.\n",
"\n",
"To perform this analysis, I got daily closing price data for Netflix from Yahoo Finance for the past 7 years. Then I took the last 500 trading days and split that into two groups. The first I used to pick a distribution for my predictions and set its parameters. The second I used for validating this approach."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<function matplotlib.pyplot.show(*args, **kw)>"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# imports datetime for picking beginning and end dates for the analysis\n",
"import datetime\n",
"# imports yahoo finance for getting historical stock prices\n",
"import yfinance as yf\n",
"# imports pandas for dataframe manipulation\n",
"import pandas as pd\n",
"# imports numpy\n",
"import numpy as np\n",
"# for data visualization\n",
"import matplotlib as mpl\n",
"# for changing the plot size in the Jupyter Notebook output\n",
"%matplotlib inline\n",
"# sets the plot size to 12x8\n",
"mpl.rcParams['figure.figsize'] = (12,8)\n",
"# for shorter lines with plotting\n",
"from matplotlib import pyplot as plt\n",
"# to hide warning messages\n",
"import warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# sets the sample period as 5 years back from 09/12/2019\n",
"end = datetime.datetime(2019, 9, 12)\n",
"start = end - datetime.timedelta(days = 7*365)\n",
"\n",
"\n",
"# gets the closing price fo Netflix for the past 5 years\n",
"my_stock = yf.Ticker('NFLX')\n",
"my_stock = pd.DataFrame(my_stock.history(start = start, end = end)['Close'])\n",
"my_stock = my_stock.rename(str.lower, axis = 'columns')\n",
"\n",
"# grabs the last 100 observations, which will be reduced to 50 for the purpose of fitting a\n",
"# distribution for Monte Carlo simulation\n",
"my_stock_resid_distr_fitting = my_stock[-500:]\n",
"# creates a training subset missing the final 100 observations, which are being withheld\n",
"my_stock_train = my_stock[~my_stock.isin(my_stock_resid_distr_fitting).all(1)]\n",
"# grabs the final 50 observations for a test set\n",
"my_stock_test = my_stock_resid_distr_fitting[-250:]\n",
"# reduces the distribution fitting dataset to 50 observations\n",
"my_stock_resid_distr_fitting = my_stock_resid_distr_fitting[~my_stock_resid_distr_fitting.isin(my_stock_test).all(1)]\n",
"\n",
"# plots the my_stock weekly closing price over the past 5 years\n",
"plt.plot(my_stock.index, my_stock.close)\n",
"plt.title('Daily Closing Price: Past 7 Years')\n",
"plt.xlabel('Date')\n",
"plt.ylabel('Closing Share Price')\n",
"plt.show"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## **II. Establishing the Order of Integration**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before modeling, the order of integration of our time series needs to be established. If it is not stationary, aka I(0), then we will have issues with auto-correlation in our residuals, which violates an essential assumption made by many statistical models (meaning our model would be bad). To determine the order of integration, Auto-Correlation Functions and Augmented-Dickey Fuller Tests can help us out.\n",
"\n",
"Note: stationary is a short way of saying that the mean and variance of the series do not vary over time."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### **B. Auto-Correlation Function Plots**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The line of the ACF shows strong postive auto-correlation for the first 450, or so, lags. Then there is a long period of negative auto-correlation. This is a good indication that the stock price is non-stationary."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# to suppress warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# sets the plot size to 12x8\n",
"mpl.rcParams['figure.figsize'] = (12,8)\n",
"\n",
"# plots the ACF for the entire train period\n",
"pd.plotting.autocorrelation_plot(my_stock_train.close)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The ACF plot for the differenced stock prices, however, looks stationary. This suggests the stock price is I(1)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1f148396710>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# to suppress warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# sets the plot size to 12x8\n",
"mpl.rcParams['figure.figsize'] = (12,8)\n",
"\n",
"# plots the ACF for the differenced data over the entire train period\n",
"pd.plotting.autocorrelation_plot(my_stock_train.close.diff().dropna())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### **B. Augmented Dickey-Fuller Tests**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The ADF tests confirm that the stock price is not stationary, but its first difference is. This means the stock price is integrated to the order 1 and will need to be differenced one time for modeling."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ADF Statistic with nc for Closing my_stock price: 1.813973\n",
"p-value: 0.983978\n",
"\n",
"ADF Statistic with c for Closing my_stock price: -0.154039\n",
"p-value: 0.943783\n",
"\n",
"ADF Statistic with ct for Closing my_stock price: -2.536304\n",
"p-value: 0.310056\n",
"\n",
"ADF Statistic with nc for Differenced Closing my_stock price: -34.769891\n",
"p-value: 0.000000\n",
"\n",
"ADF Statistic with c for Differenced Closing my_stock price: -34.881306\n",
"p-value: 0.000000\n",
"\n",
"ADF Statistic with ct for Differenced Closing my_stock price: -34.879936\n",
"p-value: 0.000000\n",
"\n"
]
}
],
"source": [
"# to suppress warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# imports the Augmented Dickey-Fuller Test for establishing the order of integration of \n",
"# time series\n",
"from statsmodels.tsa.stattools import adfuller\n",
"\n",
"# performs ADF tests with no constant, a constant, and a constant plus linear trend on\n",
"# NFLX closing share prices\n",
"for i in ['nc', 'c', 'ct']:\n",
" result = adfuller(my_stock_train.close, regression = i)\n",
" print('ADF Statistic with %s for Closing my_stock price: %f' % (i, result[0]))\n",
" print('p-value: %f' % result[1])\n",
" print('')\n",
"\n",
"# performs ADF tests with no constant, a constant, and a constant plus linear trend on\n",
"# differenced NFLX closing share prices\n",
"for i in ['nc', 'c', 'ct']:\n",
" result = adfuller(my_stock_train.close.diff().dropna(), regression = i)\n",
" print('ADF Statistic with %s for Differenced Closing my_stock price: %f' % (i, result[0]))\n",
" print('p-value: %f' % result[1])\n",
" print('')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## **III. Estimating a Simple ARIMA Model**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here I estimated a simple ARIMA model of order (1, 1, 1) on the natural logarithm of the differenced stock prices to control for heteroskedasticity. The residuals on the training data set appear stationary, but somewhere there are some big spikes giving a long tails to the distribution of residuals. As just mentioned, the distribution of residuals have long tails, and the center of the distribution is a sharp peak around zero. Because the mean of the distributions is roughly zero, it seems reasonable to proceed with this simple model. We just need to keep in mind the residuals may be differently distributed than a normal distribution because of the long tails and sharp peak."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" ARIMA Model Results \n",
"==============================================================================\n",
"Dep. Variable: D.close No. Observations: 1258\n",
"Model: ARIMA(1, 1, 1) Log Likelihood 2606.017\n",
"Method: css-mle S.D. of innovations 0.030\n",
"Date: Thu, 12 Sep 2019 AIC -5204.034\n",
"Time: 16:43:12 BIC -5183.485\n",
"Sample: 1 HQIC -5196.311\n",
" \n",
"=================================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"---------------------------------------------------------------------------------\n",
"const 0.0025 0.001 2.715 0.007 0.001 0.004\n",
"ar.L1.D.close -0.1365 0.401 -0.340 0.734 -0.923 0.650\n",
"ma.L1.D.close 0.1985 0.397 0.500 0.617 -0.580 0.976\n",
" Roots \n",
"=============================================================================\n",
" Real Imaginary Modulus Frequency\n",
"-----------------------------------------------------------------------------\n",
"AR.1 -7.3258 +0.0000j 7.3258 0.5000\n",
"MA.1 -5.0388 +0.0000j 5.0388 0.5000\n",
"-----------------------------------------------------------------------------\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0\n",
"count 1258.000000\n",
"mean -0.000002\n",
"std 0.030498\n",
"min -0.217197\n",
"25% -0.013659\n",
"50% -0.002005\n",
"75% 0.012230\n",
"max 0.346335\n"
]
}
],
"source": [
"# to suppress warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# imports the ARIMA model\n",
"from statsmodels.tsa.arima_model import ARIMA\n",
"\n",
"# fits the ARIMA model\n",
"my_stock_arima = ARIMA(np.log(my_stock_train.astype(float)), order = (1, 1, 1))\n",
"my_stock_arima_fit = my_stock_arima.fit(disp = 0)\n",
"print(my_stock_arima_fit.summary())\n",
"\n",
"# sets the plot size to 12x8\n",
"mpl.rcParams['figure.figsize'] = (12,8)\n",
"\n",
"# plot residual errors of the training data\n",
"residuals = pd.DataFrame(my_stock_arima_fit.resid)\n",
"residuals.plot()\n",
"plt.show()\n",
"residuals.plot(kind='kde')\n",
"plt.show()\n",
"print(residuals.describe())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## **IV. Picking a Distribution for Predictions**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"After choosing a simple ARIMA model, I performed a rolling forecast on one of the withheld data sets and examined the residuals. It's *roughly* bell-shaped and appears to be centered at 0. The fitting function indicates the Laplacian distribution is a reasonable distribution to use for our Monte Carlo simulations. Here is an example of automatically assuming a normal distribution getting you into trouble. Often times a different distribution is a better fit, empirically or theoretically (based on existence of bounds, etc). The Laplacian distribution is often a good fit for stock returns because of its fat tails, but again, always check first."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Test MSE: 50.913\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# to suppress warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# imports the mean squared error function\n",
"from sklearn.metrics import mean_squared_error\n",
"\n",
"# from https://machinelearningmastery.com/arima-for-time-series-forecasting-with-python/\n",
"\n",
"# creates a new dataframe that will be added to as the forecast rolls \n",
"history = np.log(my_stock_train.astype(float))\n",
"# creates an empty list that will hold predictions\n",
"predictions = []\n",
"# loops through the indexes of the set being forecased\n",
"for i in range(len(my_stock_resid_distr_fitting)):\n",
" # estimates an ARIMA model of order (1,1,1)\n",
" model = ARIMA(history, order = (1,1,1))\n",
" # fits the model\n",
" model_fit = model.fit(disp = 0)\n",
" # forecasts the next period\n",
" output = model_fit.forecast()\n",
" # takes the predicted value and saves it in yhat\n",
" yhat = np.e ** output[0]\n",
" # appends yhat to the list of predictions\n",
" predictions.append(yhat)\n",
" # grabs the observation at the ith index\n",
" obs = my_stock_resid_distr_fitting[i : i + 1]\n",
" # appends the observation to the estimation data set\n",
" history = history.append(np.log(obs.astype(float)))\n",
"\n",
"# prints the MSE of the model for the rolling forecast period\n",
"error = mean_squared_error(my_stock_resid_distr_fitting, predictions)\n",
"print('Test MSE: %.3f' % error)\n",
"\n",
"# converts the predictions list to a pandas dataframe with the same index as the actual values\n",
"# for plotting purposes\n",
"predictions = pd.DataFrame(predictions)\n",
"predictions.index = my_stock_resid_distr_fitting.index\n",
"\n",
"# sets the plot size to 12x8\n",
"mpl.rcParams['figure.figsize'] = (12,8)\n",
"\n",
"# plots the predicted and actual stock prices \n",
"plt.plot(my_stock_resid_distr_fitting)\n",
"plt.plot(predictions, color = 'red')\n",
"plt.xlabel('Date')\n",
"plt.ylabel('Dollars')\n",
"plt.title('Predicted vs. Actual Closing Weekly Stock Price')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1f148357240>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# to suppress warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# sets the plot size to 12x8\n",
"mpl.rcParams['figure.figsize'] = (12,8)\n",
"\n",
"# plots the residuals\n",
"tune_residuals = my_stock_resid_distr_fitting.close - predictions[0]\n",
"tune_residuals.plot(kind = 'kde')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"count 250.000000\n",
"mean 0.022499\n",
"std 7.149600\n",
"min -27.462273\n",
"25% -3.372016\n",
"50% -0.210684\n",
"75% 3.462415\n",
"max 27.783077\n",
"dtype: float64"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# to suppress warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# produces a summary of the residuals\n",
"tune_residuals.astype(float).describe()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Fitted alpha distribution with error=0.3986427981014272)\n",
"Fitted anglit distribution with error=0.04543978898101991)\n",
"Fitted arcsine distribution with error=0.0967647644861612)\n",
"Fitted argus distribution with error=0.0574353584723472)\n",
"Fitted beta distribution with error=0.016713838486536552)\n",
"Fitted betaprime distribution with error=0.016673352570134393)\n",
"Fitted bradford distribution with error=0.07095563075146454)\n",
"Fitted burr distribution with error=0.029585365298671853)\n",
"Fitted burr12 distribution with error=0.012102792137395966)\n",
"Fitted cauchy distribution with error=0.010885486275246041)\n",
"Fitted chi distribution with error=0.10141737234552045)\n",
"Fitted chi2 distribution with error=0.29679980269959194)\n",
"Fitted cosine distribution with error=0.03509399038669166)\n",
"Fitted crystalball distribution with error=0.01390419367420572)\n",
"Fitted dgamma distribution with error=0.009306132765515198)\n",
"Fitted dweibull distribution with error=0.00967396446458837)\n",
"Fitted erlang distribution with error=0.01689428706027455)\n",
"Fitted expon distribution with error=0.08186766741337398)\n",
"Fitted exponnorm distribution with error=0.016002671273311186)\n",
"Fitted exponpow distribution with error=0.15494580925516885)\n",
"Fitted exponweib distribution with error=0.20728396348867242)\n",
"Fitted f distribution with error=0.24440757271897628)\n",
"Fitted fatiguelife distribution with error=0.01649101905834446)\n",
"Fitted fisk distribution with error=0.29402283991613704)\n",
"Fitted foldcauchy distribution with error=0.3498180765884026)\n",
"Fitted foldnorm distribution with error=0.6455617488011087)\n",
"Fitted frechet_l distribution with error=0.269271116230118)\n",
"Fitted frechet_r distribution with error=0.2685309406762277)\n",
"Fitted gamma distribution with error=0.016941871516779776)\n",
"Fitted gausshyper distribution with error=0.05922620900649582)\n",
"Fitted genexpon distribution with error=0.07925649402276129)\n",
"Fitted genextreme distribution with error=0.22943830061187925)\n",
"Fitted gengamma distribution with error=0.2224856180275161)\n",
"Fitted genhalflogistic distribution with error=0.056474100316919164)\n",
"Fitted genlogistic distribution with error=0.01150803250021771)\n",
"Fitted gennorm distribution with error=0.009146417510223782)\n",
"Fitted genpareto distribution with error=0.6013962140299675)\n",
"Fitted gilbrat distribution with error=0.07113908297613793)\n",
"Fitted gompertz distribution with error=0.5574509883751668)\n",
"Fitted gumbel_l distribution with error=0.027570841230644235)\n",
"Fitted gumbel_r distribution with error=0.029468728998022768)\n",
"Fitted halfcauchy distribution with error=0.0773505422519097)\n",
"Fitted halfgennorm distribution with error=0.10766755030531663)\n",
"Fitted halflogistic distribution with error=0.07344670739432277)\n",
"Fitted halfnorm distribution with error=0.0720407258302391)\n",
"Fitted hypsecant distribution with error=0.009891735309723853)\n",
"Fitted invgamma distribution with error=0.017539944152829223)\n",
"Fitted invgauss distribution with error=0.021492633331981086)\n",
"Fitted invweibull distribution with error=0.029490125613205943)\n",
"Fitted johnsonsb distribution with error=0.016682852606315586)\n",
"Fitted johnsonsu distribution with error=0.008807122401678334)\n",
"Fitted kappa3 distribution with error=0.05688744981908669)\n",
"Fitted kappa4 distribution with error=0.06906878372530004)\n",
"Fitted ksone distribution with error=nan)\n",
"Fitted kstwobign distribution with error=1.1408855402067018e+45)\n",
"Fitted laplace distribution with error=0.009133635200146602)\n",
"Fitted levy distribution with error=0.07927702087877887)\n",
"Fitted levy_l distribution with error=0.0791563961031317)\n",
"SKIPPED levy_stable distribution (taking more than 30 seconds)\n",
"Fitted loggamma distribution with error=0.01666950626606528)\n",
"Fitted logistic distribution with error=0.011327879624147196)\n",
"Fitted loglaplace distribution with error=0.2630108675222178)\n",
"Fitted lognorm distribution with error=0.016518306599070772)\n",
"Fitted lomax distribution with error=0.07448212642981542)\n",
"Fitted maxwell distribution with error=0.039315808214962826)\n",
"Fitted mielke distribution with error=0.010250768438340144)\n",
"Fitted moyal distribution with error=0.037538602294536344)\n",
"Fitted nakagami distribution with error=0.1000226499879551)\n",
"Fitted ncf distribution with error=0.06328580926524952)\n",
"Fitted nct distribution with error=0.009229528850599092)\n",
"Fitted ncx2 distribution with error=0.017386883479065685)\n",
"Fitted norm distribution with error=0.016592335180342588)\n",
"Fitted norminvgauss distribution with error=0.009073776774410793)\n",
"Fitted pareto distribution with error=0.08569469727392075)\n",
"Fitted pearson3 distribution with error=0.01666046297919349)\n",
"Fitted powerlaw distribution with error=0.06611726402812963)\n",
"Fitted powerlognorm distribution with error=0.01653482558574912)\n",
"Fitted powernorm distribution with error=0.016530477394218004)\n",
"Fitted rayleigh distribution with error=0.05007174407199912)\n",
"Fitted rdist distribution with error=0.07542264217677425)\n",
"Fitted recipinvgauss distribution with error=0.01760675610057699)\n",
"Fitted reciprocal distribution with error=1.1278340893651713)\n",
"Fitted rice distribution with error=0.5420554827452849)\n",
"SKIPPED rv_continuous distribution (taking more than 30 seconds)\n",
"SKIPPED rv_histogram distribution (taking more than 30 seconds)\n",
"Fitted semicircular distribution with error=0.05509971024404405)\n",
"Fitted skewnorm distribution with error=0.01653518226649937)\n",
"Fitted t distribution with error=0.009198597912322791)\n",
"Fitted trapz distribution with error=0.07296553829609224)\n",
"Fitted triang distribution with error=0.03657212847993335)\n",
"Fitted truncexpon distribution with error=0.06989247852451158)\n",
"Fitted truncnorm distribution with error=0.0997100746954121)\n",
"Fitted tukeylambda distribution with error=0.009094896221208976)\n",
"Fitted uniform distribution with error=0.06694519736384924)\n",
"Fitted vonmises distribution with error=1.442046327922535e+58)\n",
"Fitted vonmises_line distribution with error=0.01748916808433698)\n",
"Fitted wald distribution with error=0.0681123863410969)\n",
"Fitted weibull_max distribution with error=0.269271116230118)\n",
"Fitted weibull_min distribution with error=0.2685309406762277)\n",
"Fitted wrapcauchy distribution with error=nan)\n"
]
},
{
"data": {
"text/plain": [
"<bound method Fitter.summary of <fitter.fitter.Fitter object at 0x000001F14CDCBFD0>>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# to suppress warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# imports the fitter function and produces estimated fits for our residuals\n",
"from fitter import Fitter\n",
"\n",
"f = Fitter(tune_residuals)\n",
"f.fit()\n",
"f.summary"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## **V. Using Monte Carlo Simulation to Predict Stock Price Intervals**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can generate empirically derived prediction intervals using our chosen distribution (Laplacian), mean (the residuals were centered at zero, so this will just be our predicted stock price), beta (calculated from the residuals as the mean absolute distance from the mean), and number of simulations, which is chosen by the user. I chose to do 1000. There are techniques to pick a number of simulations to ensure that the simulated distribution converges towards the actual distribution, but that is for another article. Here, I'm just doing 1000 because I think it should be enough. A little handwavey, I know."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# creates a function to do MC simulation with a Laplacian distribution\n",
"def laplace_monte_carlo(mean, residuals, n_sims):\n",
" # gets the estimated beta or mean absolute distance from the mean\n",
" beta = (sum(abs(residuals - np.mean(residuals))) \n",
" / len(residuals))\n",
" # uses the numpy function to generate an array of simulated values\n",
" est_range = np.random.laplace(mean, beta, n_sims)\n",
" # converts the array to a list\n",
" est_range = list(est_range)\n",
" # returns the simulated values\n",
" return(est_range)\n",
"\n",
"def roll_forecast_nmc(train, test, std_dev, n_sims):\n",
" # creates a new dataframe that will be added to as the forecast rolls \n",
" history = np.log(train.astype(float))\n",
" # creates an empty list that will hold predictions\n",
" predictions = []\n",
" # loops through the indexes of the set being forecased\n",
" for i in range(len(test)):\n",
" # estimates an ARIMA model of order (1,1,0)\n",
" model = ARIMA(history, order = (1,1,1))\n",
" # fits the model\n",
" model_fit = model.fit(disp = 0)\n",
" # forecasts the next period\n",
" output = model_fit.forecast()\n",
" # takes the predicted value and saves it in yhat\n",
" yhat = np.e ** output[0]\n",
" # performs monte carlo simulation using the predicted price as the mean, user-specified\n",
" # standard deviation, and number of simulations\n",
" yhat_range = laplace_monte_carlo(yhat, std_dev, n_sims)\n",
" # appends yhat_range to the list of predictions\n",
" predictions.append([float(i) for i in yhat_range])\n",
" # grabs the observation at the ith index\n",
" obs = test[i : i + 1]\n",
" # appends the observation to the estimation data set\n",
" history = history.append(np.log(obs.astype(float)))\n",
"\n",
" # converts the predictions list to a pandas dataframe with the same index as the actual \n",
" # values for plotting purposes\n",
" predictions = pd.DataFrame(predictions)\n",
" predictions.index = my_stock_resid_distr_fitting.index\n",
" # converts all the estimated yhats in each column to one list per row\n",
" predictions['predicted_range'] = predictions.values.tolist()\n",
" # grabs only the column with all values in a list\n",
" predictions = pd.DataFrame(predictions['predicted_range'])\n",
" \n",
" # returns predictions\n",
" return(predictions)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# attaches the data withheld for investigating the forecast residuals back to the training\n",
"# data set to avoid a large error on the first forecast\n",
"my_stock_train = my_stock_train.append(my_stock_resid_distr_fitting)\n",
"\n",
"\n",
"# produces a rolling forecast with prediction intervals using 1000 MC sims\n",
"test_preds = roll_forecast_nmc(my_stock_train, \n",
" my_stock_test, \n",
" tune_residuals,\n",
" 1000)"
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"The percentage of actual week ahead stock prices within our prediction interval is 100.0%. That is pretty good, especially for our simple ARIMA model that hasn't been tuned. Using a different model that accounted for financial statement data, sentiment analysis of tweets, et cetera could produce a better model, but this simple one worked decently well."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Percentage of Actual Stock Prices in Predicted Stock Price Range: 100.000000\n"
]
}
],
"source": [
"# creates an empty list\n",
"in_prediction_interval = []\n",
"# loops through the rows in the testing data set\n",
"for i in range(len(my_stock_test)):\n",
" # appends true if the actual price is in the interval of predicted prices and false\n",
" # otherwise\n",
" in_prediction_interval.append(np.where(min(test_preds.predicted_range[i]) <= \n",
" my_stock_test.close[i]\n",
" <= max(test_preds.predicted_range[i]), \n",
" True, False))\n",
"# prints the percentage of actual prices in the prediction intervals \n",
"print('Percentage of Actual Stock Prices in Predicted Stock Price Range: %f' % \n",
" (100 * sum(in_prediction_interval) / len(in_prediction_interval)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I plotted the prediction intervals along with the actual stock prices and the actual price does appear to generally be in the middle of our prediction intervals, which is exactly what we want."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# creates empty lists to append to with minimum and maximum values for each weeks prediction\n",
"min_range = []\n",
"max_range = []\n",
"\n",
"# loops through the rows in test_preds\n",
"for i in range(len(test_preds)):\n",
" # appends to the list the min or max value as appropriate\n",
" min_range.append(min(test_preds.predicted_range[i]))\n",
" max_range.append(max(test_preds.predicted_range[i]))\n",
"\n",
"# converts the lists to data frames and makes their indexes match up with the dates they're\n",
"# predicting\n",
"min_range = pd.DataFrame(min_range)\n",
"min_range.index = my_stock_test.index\n",
"max_range = pd.DataFrame(max_range)\n",
"max_range.index = my_stock_test.index\n",
"\n",
"# plots the actual stock price with prediction intervals\n",
"plt.plot(my_stock_test)\n",
"plt.plot(min_range, color = 'red')\n",
"plt.plot(max_range, color = 'red')\n",
"plt.xlabel('Date')\n",
"plt.ylabel('Dollars')\n",
"plt.title('Actual Closing Weekly Stock Price with Prediction Intervals')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## **VI. Conclusions**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So what are potential applications of pairing Monte Carlo simulation and time series modeling in investing? Prediction intervals generated using Monte Carlo simulation can be used to predict the probability that an option is in the money or if a stock is a buy, hold, or sell over you chosen time horizon (**again, please do not start trying to trade options using this model or pursue any other type of investing strategy without careful consideration and backtesting**). I did this below where I calculated the probability that the stock price on 09/12/2019 is greater than or equal to 290 and got the probability of 36.7%. "
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability Actual Stock Price is above Strike Price: 0.367000\n"
]
}
],
"source": [
"# sets a target price to see the probability that the actual stock price is greater than or \n",
"# equal to this target\n",
"target_price = 290\n",
"# creates a list of True values where the simulated price is above or equal to the target price\n",
"# and False where it is below\n",
"above_target = [i >= target_price for i in test_preds.predicted_range[len(test_preds) - 1]]\n",
"# prints the probability\n",
"print('Probability Actual Stock Price is above Strike Price: %f' % \n",
" (sum(above_target) / len(above_target)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The proliferation of free statistical software and open source programming languages is empowering a generation of investors with some statistical knowledge to take advantage of techniques and strategies that were previously the domain of institutional investors with teams of PhDs. Even individual investors without strong machine learning or statistics backgrounds will be able to take advantage of these services as platforms like https://malgo.io/ begin to allow regular investors to get machine learning powered securities recommendations.\n",
"\n",
"One question I keep coming back to is as these tools gain deeper adoption, how will that change the structure of the markets? Will finding excess returns become more difficult as more investors adopt rigorous investment strategies? Will there be unforeseen consequences like the Flash Crash? Or will people continue going to low-fee market tracking ETFs to grow with the market without needing to worry about actively managing money? It's an open question, but it is defininetly an exciting time to watch the intersection of data science and finance."
]
}
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