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Sign in[Submit an Article](https://write.insightmediagroup.io) [Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/) * * * [Write For TDS](https://towardsdatascience.com/submissions/) [LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search [Data Science](https://towardsdatascience.com/category/data-science/) # Time-Series Forecasting: Predicting Stock Prices Using An ARIMA Model In this post I show you how to predict the TESLA stock price using a forecasting ARIMA model [Serafeim Loukas, PhD](https://towardsdatascience.com/author/seralouk/) July 23, 20206 min read ![ARIMA model performance on the test set](../images/000.png) ARIMA model performance on the test set ## 1. Introduction ### 1.1. Time-series & forecasting models **Time-series forecasting** models are the models that are capable to **predict** **future values** based on **previously** **observed** **values**. Time-series forecasting is widely used for **non-stationary data**. **Non-stationary data** are called the data whose statistical properties e.g. the mean and standard deviation are not constant over time but instead, these metrics vary over time. These non-stationary input data (used as input to these models) are usually called **time-series.** Some examples of time-series include the temperature values over time, stock price over time, price of a house over time etc. So, the input is a **signal** (time-series) that is **defined by observations taken sequentially in time**. > A time series is a sequence of observations taken sequentially in time. ![An example of a time-series. Plot created by the author in Python.](../images/001.png) An example of a time-series. Plot created by the author in Python. **Observation: Time-series** data is recorded on a **discrete** **time** **scale**. **Disclaimer** : There have been attempts to predict stock prices using time series analysis algorithms, though they still cannot be used to place bets in the real market. This is just a tutorial article that does not intent in any way to "direct" people into buying stocks. * * * If you're passionate about diving deeper into machine learning with Python and sklearn, I highly recommend checking out [**this book**](https://amzn.to/3t4YB2d); it's a game-changer in breaking down complex topics into digestible insights. > [**Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques...**](https://amzn.to/3t4YB2d) * * * ## 2. The AutoRegressive Integrated Moving Average (ARIMA) model A famous and widely used forecasting method for time-series prediction is the **AutoRegressive Integrated Moving Average (ARIMA)** model. **ARIMA** models are capable of capturing a suite of different standard temporal structures in time-series data. ### Terminology Let's break down these terms: * **AR: < Auto Regressive >** means that the model **uses the dependent relationship between an observation and some predefined number of lagged observations** (also known as "time lag" or "lag"). * **I: < Integrated >** means that the model employs **differencing of raw observations** (e.g. it subtracts an observation from an observation at the previous time step) in order to make the time-series **stationary.MA** : * _**MA: < Moving Average >**_ means that the model exploits the **relationship between the residual error and the observations.** ### Model parameters The standard ARIMA models expect as input parameters 3 arguments i.e. p,d,q. * **p** is the **number of lag observations.** * **d** is the **degree of differencing.** * **q** is the **size/width of the moving average window.** * * * * **NEW** : After a great deal of hard work and staying behind the scenes for quite a while, we're excited to now offer our expertise through a platform, the "[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\))" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning. * Another resource. Learn Data Science and ML with the help of an 🤖 AI-powered tutor. Start here h[ttps://aigents.co/learn ](https://aigents.co/learn)choose a topic and he will show up where you need him. No paywall, no signups, no ads. * * * ## 3. Getting the stock price history data Thanks to **Yahoo finance** we can get the data for **free**. Use the following link to get the stock price history of **TESLA** : [https://finance.yahoo.com/quote/TSLA/history?period1=1436486400&period2=1594339200&interval=1d&filter=history&frequency=1d](https://finance.yahoo.com/quote/TSLA/history?period1=1436486400&period2=1594339200&interval=1d&filter=history&frequency=1d) You should see the following: ![](../images/body-4632f022c0c2ea7a4a71.png) Click on the **Download** and save the **.csv** file locally on your computer. The data are from **2015** till now (**2020**) ! * * * ## 4. Python working example _Modules needed: Numpy, Pandas,_ Statsmodels _, Scikit-Learn_ **4.1. Load & inspect the data** Our **imports** : text ``` import numpy as np import pandas as pd import matplotlib.pyplot as plt from pandas.plotting import lag_plot from pandas import datetime from statsmodels.tsa.arima_model import ARIMA from sklearn.metrics import mean_squared_error ``` Now let's **load** the TESLA stock history **data** : text ``` df = pd.read_csv("TSLA.csv") df.head(5) ``` ![](../images/body-6891cf82dea41f5aeba9.png) * Our target variable will be the **Close** value. ### Before building the ARIMA model, let's see if there is some cross-correlation in out data. text ``` plt.figure() lag_plot(df['Open'], lag=3) plt.title('TESLA Stock - Autocorrelation plot with lag = 3') plt.show() ``` ![TESLA Stock - Autocorrelation plot with lag = 3](../images/002.png) TESLA Stock - Autocorrelation plot with lag = 3 We can now confirm that **ARIMA** is going to be a good model to be applied to this type of data (there is auto-correlation in the data). Finally, let's **plot the stock price evolution over time.** text ``` plt.plot(df["Date"], df["Close"]) plt.xticks(np.arange(0,1259, 200), df['Date'][0:1259:200]) plt.title("TESLA stock price over time") plt.xlabel("time") plt.ylabel("price") plt.show() ``` ![](../images/body-47c2d97345e32166d9a9.png) **4.2. Build the predictive ARIMA model** Next, let's **divide** the data into a **training** (70 % ) and **test** (30%) set. For this tutorial we select the following **ARIMA parameters: p=4, d=1 and q=0.** text ``` train_data, test_data = df[0:int(len(df)*0.7)], df[int(len(df)*0.7):] ``` text ``` training_data = train_data['Close'].values test_data = test_data['Close'].values ``` text ``` history = [x for x in training_data] model_predictions = [] N_test_observations = len(test_data) ``` text ``` for time_point in range(N_test_observations): model = ARIMA(history, order=(4,1,0)) model_fit = model.fit(disp=0) output = model_fit.forecast() yhat = output[0] model_predictions.append(yhat) true_test_value = test_data[time_point] history.append(true_test_value) ``` text ``` MSE_error = mean_squared_error(test_data, model_predictions) print('Testing Mean Squared Error is {}'.format(MSE_error)) ``` ### Summary of the code * We split the training dataset into train and test sets and we use the train set to fit the model, and generate a prediction **for each element on the test set**. * **A rolling forecasting procedure is required given the dependence on observations in prior time steps for differencing and the AR model. To this end, we re-create the ARIMA model after each new observation is received.** * Finally, we manually keep track of all observations in a list called **history** that is seeded with the training data and to which new observations are appended at each iteration. Testing Mean Squared Error is 741.0594879572484 > The MSE of the test set is quite large denoting that the precise prediction is a hard problem. However, this is the average squared value across all the test set predictions. Let's **visualize** the predictions to understand the performance of the model more. text ``` test_set_range = df[int(len(df)*0.7):].index ``` text ``` plt.plot(test_set_range, model_predictions, color='blue', marker='o', linestyle='dashed',label='Predicted Price') ``` text ``` plt.plot(test_set_range, test_data, color='red', label='Actual Price') ``` text ``` plt.title('TESLA Prices Prediction') plt.xlabel('Date') plt.ylabel('Prices') plt.xticks(np.arange(881,1259,50), df.Date[881:1259:50]) plt.legend() plt.show() ``` ![ARIMA model performance on the test set](../images/003.png) ARIMA model performance on the test set ### Not so bad right? Our ARIMA model results in appreciable results. This model offers a good prediction accuracy and to be relatively fast compared to other alternatives, in terms of training/fitting time and complexity. That's all folks ! Hope you liked this article! * * * If you're passionate about diving deeper into machine learning with Python and sklearn, I highly recommend checking out [**this book**](https://amzn.to/3t4YB2d); it's a game-changer in breaking down complex topics into digestible insights. > [**Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques...**](https://amzn.to/3t4YB2d) * * * ## Stay tuned & support this effort If you liked and found this article useful, **follow** me to be able to see all my new posts. Questions? Post them as a comment and I will reply as soon as possible. We offer our expertise through a platform, the "[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\))" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning. * * * ## My previous articles that you might also like: [**LSTM Time-Series Forecasting: Predicting Stock Prices Using An LSTM Model**](https://towardsdatascience.com/lstm-time-series-forecasting-predicting-stock-prices-using-an-lstm-model-6223e9644a2f) > [**LSTM Time-Series Forecasting: Predicting Stock Prices Using An LSTM Model**](https://towardsdatascience.com/lstm-time-series-forecasting-predicting-stock-prices-using-an-lstm-model-6223e9644a2f) [**Time-Series Forecasting: Predicting Stock Prices Using Facebook's Prophet Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-facebooks-prophet-model-9ee1657132b5) > [**Time-Series Forecasting: Predicting Stock Prices Using Facebook's Prophet Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-facebooks-prophet-model-9ee1657132b5) * * * ## References [1] * * * ## Other posts > [**The Best FREE Data Science Resources: FREE Books & Online Courses**](https://medium.com/@seralouk/the-best-free-data-science-resources-free-books-online-courses-9c4a2df194e5) > [**ROC Curve Explained using a COVID-19 hypothetical example: Binary & Multi-Class Classification...**](https://towardsdatascience.com/roc-curve-explained-using-a-covid-19-hypothetical-example-binary-multi-class-classification-bab188ea869c) > [**Support Vector Machines (SVM) clearly explained: A python tutorial for classification problems...**](https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8) > [**PCA clearly explained - How, when, why to use it and feature importance: A guide in Python**](https://towardsdatascience.com/pca-clearly-explained-how-when-why-to-use-it-and-feature-importance-a-guide-in-python-7c274582c37e) > [**Everything you need to know about Min-Max normalization in Python**](https://towardsdatascience.com/everything-you-need-to-know-about-min-max-normalization-in-python-b79592732b79) > [**How Scikit-Learn's StandardScaler works**](https://towardsdatascience.com/how-and-why-to-standardize-your-data-996926c2c832) ## Register Now to Continue Reading ### Unlock Towards Data Science with a Free Account All articles on Towards Data Science are available to registered users. 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