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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 July 23, 20206 min read ARIMA model performance on the test set 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. 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; 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...

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:

Model parameters

The standard ARIMA models expect as input parameters 3 arguments i.e. p,d,q.

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 You should see the following: 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)

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 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()

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

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 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; 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...

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" on Patreon (https://www.patreon.com/TheDataScienceHub). 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

LSTM Time-Series Forecasting: Predicting Stock Prices Using An LSTM Model Time-Series Forecasting: Predicting Stock Prices Using Facebook's Prophet Model Time-Series Forecasting: Predicting Stock Prices Using Facebook's Prophet Model

References

[1] https://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average

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