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Stock Market Price Trend Prediction Using Time Series Forecasting

This article was published as a part of the Data Science Blogathon.

Introduction

Time series forecasting is used to predict future values based on previously observed values and one of the best tools for trend analysis and future prediction.

 

What is time-series data?

It is recorded at regular time intervals, and the order of these data points is important. Therefore, any predictive model based on time series data will have time as an independent variable. The output of a model would be the predicted value or classification at a specific time.

Time series analysis vs time series forecasting

Let’s talk about some possible confusion about the Time Series Analysis and Forecasting. Time series forecasting is an example of predictive modeling whereas time series analysis is a form of descriptive modeling.

For a new investor general research which is associated with the stock or share market is not enough to make the decision. The common trend towards the stock market among the society is highly risky for investment so most of the people are not able to make decisions based on common trends. The seasonal variance and steady flow of any index will help both existing and new investors to understand and make a decision to invest in the share market.

To solve this kind of problem time series forecasting is the best technique.

 

Stock market

Stock markets are where individual and institutional investors come together to buy and sell shares in a public venue. Nowadays these exchanges exist as electronic marketplaces.

That supply and demand help determine the price for each security or the levels at which stock market participants — investors and traders — are willing to buy or sell.

The concept behind how the stock market works is pretty simple. Operating much like an auction house, the stock market enables buyers and sellers to negotiate prices and make trades.

Definition of ‘Stock’

A Stock or share (also known as a company’s “equity”) is a financial instrument that represents ownership in a company

 

Machine learning in the stock market

The stock market is very unpredictable, any geopolitical change can impact the share trend of stocks in the share market, recently we have seen how covid-19 has impacted the stock prices, which is why on financial data doing a  reliable trend analysis is very difficult. The most efficient way to solve this kind of issue is with the help of Machine learning and Deep learning.

In this tutorial, we will be solving this problem with ARIMA Model.

A popular and widely used statistical method for time series forecasting is the ARIMA model. It is one of the most popular models to predict linear time series data. This model has been used extensively in the field of finance and economics as it is known to be robust, efficient, and has a strong potential for short-term share market prediction. Exponential smoothing and ARIMA models are the two most widely used approaches to time series forecasting and provide complementary approaches to the problem. While exponential smoothing models are based on a description of the trend and seasonality in the data, ARIMA models aim to describe the auto-correlation(Autocorrelation is the degree of similarity between a given time series and a lagged version of itself over successive time intervals) in the data.

To know about seasonality please refer to my previous blog, And to get a basic understanding of ARIMA I would recommend you to go through this blog, this will help you to get a better understanding of how Time Series analysis works.

Implementing stock price forecasting

I will be using nsepy library to extract the historical data for SBIN.

Imports

import os
import warnings
warnings.filterwarnings('ignore')
from pylab import rcParams
rcParams['figure.figsize'] = 10, 6
from statsmodels.tsa.stattools import adfuller
from statsmodels.tsa.seasonal import seasonal_decompose
from statsmodels.tsa.arima_model import ARIMA
from pmdarima.arima import auto_arima
from sklearn.metrics import mean_squared_error, mean_absolute_error
import math
import numpy as np
from nsepy import get_history
from datetime import date
import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd
Run the below code to extract the historical data:
sbin = get_history(symbol='SBIN',
                   start=date(2000,1,1),
                   end=date(2020,11,1))
sbin.head()

 

Time Series forecasting head

The data shows the stock price of SBIN from 2020-1-1 to 2020-11-1. The goal is to create a model that will forecast
the closing price of the stock.

Let us create a visualization which will show per day closing price of the stock-

plt.figure(figsize=(10,6))
plt.grid(True)
plt.xlabel('Dates')
plt.ylabel('Close Prices')
plt.plot(sbin['Close'])
plt.title('SBIN closing price')
plt.show()
SBIN Time Series forecasting
plt.figure(figsize=(10,6))
df_close = sbin['Close']
df_close.plot(style='k.')
plt.title('Scatter plot of closing price')
plt.show()

 

Time Series forecasting - Scatter plot
plt.figure(figsize=(10,6))
df_close = sbin['Close']
df_close.plot(style='k.',kind='hist')
plt.title('Hisogram of closing price')
plt.show()

 

Histogram

First, we need to check if a series is stationary or not because time series analysis only works with stationary data.

Testing For Stationarity:

To identify the nature of the data, we will be using the null hypothesis.

H0: The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

H1: The alternative hypothesis: It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0.

#Ho: It is non-stationary
#H1: It is stationary

If we fail to reject the null hypothesis, we can say that the series is non-stationary. This means that the series can be linear.

If both mean and standard deviation are flat lines(constant mean and constant variance), the series becomes stationary.

from statsmodels.tsa.stattools import adfuller
def test_stationarity(timeseries):
    #Determing rolling statistics
    rolmean = timeseries.rolling(12).mean()
    rolstd = timeseries.rolling(12).std()
    #Plot rolling statistics:
    plt.plot(timeseries, color='yellow',label='Original')
    plt.plot(rolmean, color='red', label='Rolling Mean')
    plt.plot(rolstd, color='black', label = 'Rolling Std')
    plt.legend(loc='best')
    plt.title('Rolling Mean and Standard Deviation')
    plt.show(block=False)
    print("Results of dickey fuller test")
    adft = adfuller(timeseries,autolag='AIC')
    # output for dft will give us without defining what the values are.
    #hence we manually write what values does it explains using a for loop
    output = pd.Series(adft[0:4],index=['Test Statistics','p-value','No. of lags used','Number of observations used'])
    for key,values in adft[4].items():
        output['critical value (%s)'%key] =  values
    print(output)

test_stationarity(sbin['Close'])

 

Rolling mean and SD - Time Series forecasting
After analysing the above graph, we can see the increasing mean and standard deviation and hence our series is not stationary.
Results of dickey fuller test
Test Statistics                  -1.914523
p-value                           0.325260
No. of lags used                  3.000000
Number of observations used    5183.000000
critical value (1%)              -3.431612
critical value (5%)              -2.862098
critical value (10%)             -2.567067
dtype: float64

We see that the p-value is greater than 0.05 so we cannot reject the Null hypothesis. Also, the test statistics is greater than the critical values. so the data is non-stationary.

For time series analysis we separate Trend and Seasonality from the time series.

result = seasonal_decompose(df_close, model='multiplicative', freq = 30)
fig = plt.figure()  
fig = result.plot()  
fig.set_size_inches(16, 9)

 

Time Series forecasting seasonality
from pylab import rcParams
rcParams['figure.figsize'] = 10, 6
df_log = np.log(sbin['Close'])
moving_avg = df_log.rolling(12).mean()
std_dev = df_log.rolling(12).std()
plt.legend(loc='best')
plt.title('Moving Average')
plt.plot(std_dev, color ="black", label = "Standard Deviation")
plt.plot(moving_avg, color="red", label = "Mean")
plt.legend()
plt.show()
Time Series forecasting - moving average

Now we are going to create an ARIMA model and will train it with the closing price of the stock on the train data. So let us split the data into training and test set and visualize it.

train_data, test_data = df_log[3:int(len(df_log)*0.9)], df_log[int(len(df_log)*0.9):]
plt.figure(figsize=(10,6))
plt.grid(True)
plt.xlabel('Dates')
plt.ylabel('Closing Prices')
plt.plot(df_log, 'green', label='Train data')
plt.plot(test_data, 'blue', label='Test data')
plt.legend()
train and test
model_autoARIMA = auto_arima(train_data, start_p=0, start_q=0,
test='adf',       # use adftest to find optimal 'd'
max_p=3, max_q=3, # maximum p and q
m=1,              # frequency of series
d=None,           # let model determine 'd'
seasonal=False,   # No Seasonality
start_P=0, 
D=0, 
trace=True,
error_action='ignore',  
suppress_warnings=True, 
stepwise=True)
print(model_autoARIMA.summary())
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=-16607.561, Time=2.19 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=-16607.961, Time=0.95 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=-16608.035, Time=2.27 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=-16609.560, Time=0.39 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=-16606.477, Time=2.77 sec

Best model:  ARIMA(0,1,0)(0,0,0)[0]          
Total fit time: 9.079 seconds
                               SARIMAX Results                                
==============================================================================
Dep. Variable:                      y   No. Observations:                 4665
Model:               SARIMAX(0, 1, 0)   Log Likelihood                8305.780
Date:                Tue, 24 Nov 2020   AIC                         -16609.560
Time:                        20:08:50   BIC                         -16603.113
Sample:                             0   HQIC                        -16607.293
                               - 4665                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
sigma2         0.0017   1.06e-06   1566.660      0.000       0.002       0.002
===================================================================================
Ljung-Box (Q):                       24.41   Jarque-Bera (JB):         859838819.58
Prob(Q):                              0.98   Prob(JB):                         0.00
Heteroskedasticity (H):               7.16   Skew:                           -37.54
Prob(H) (two-sided):                  0.00   Kurtosis:                      2105.12
===================================================================================
model_autoARIMA.plot_diagnostics(figsize=(15,8))
plt.show()
residual plots
model = ARIMA(train_data, order=(3, 1, 2))
fitted = model.fit(disp=-1)
print(fitted.summary())
                             ARIMA Model Results                              
==============================================================================
Dep. Variable:                D.Close   No. Observations:                 4664
Model:                 ARIMA(3, 1, 2)   Log Likelihood                8309.178
Method:                       css-mle   S.D. of innovations              0.041
Date:                Tue, 24 Nov 2020   AIC                         -16604.355
Time:                        20:09:37   BIC                         -16559.222
Sample:                             1   HQIC                        -16588.481
                                                                              
=================================================================================
                    coef    std err          z      P>|z|      [0.025      0.975]
---------------------------------------------------------------------------------
const          8.761e-06      0.001      0.015      0.988      -0.001       0.001
ar.L1.D.Close     1.3689      0.251      5.460      0.000       0.877       1.860
ar.L2.D.Close    -0.7118      0.277     -2.567      0.010      -1.255      -0.168
ar.L3.D.Close     0.0094      0.021      0.445      0.657      -0.032       0.051
ma.L1.D.Close    -1.3468      0.250     -5.382      0.000      -1.837      -0.856
ma.L2.D.Close     0.6738      0.282      2.391      0.017       0.122       1.226
                                    Roots                                    
=============================================================================
                  Real          Imaginary           Modulus         Frequency
-----------------------------------------------------------------------------
AR.1            0.9772           -0.6979j            1.2008           -0.0987
AR.2            0.9772           +0.6979j            1.2008            0.0987
AR.3           74.0622           -0.0000j           74.0622           -0.0000
MA.1            0.9994           -0.6966j            1.2183           -0.0969
MA.2            0.9994           +0.6966j            1.2183            0.0969
-----------------------------------------------------------------------------
# Forecast

fc, se, conf = fitted.forecast(519, alpha=0.05)  # 95% confidence
fc_series = pd.Series(fc, index=test_data.index)
lower_series = pd.Series(conf[:, 0], index=test_data.index)
upper_series = pd.Series(conf[:, 1], index=test_data.index)
plt.figure(figsize=(12,5), dpi=100)
plt.plot(train_data, label='training')
plt.plot(test_data, color = 'blue', label='Actual Stock Price')
plt.plot(fc_series, color = 'orange',label='Predicted Stock Price')
plt.fill_between(lower_series.index, lower_series, upper_series, 
                 color='k', alpha=.10)
plt.title('SBIN Stock Price Prediction')
plt.xlabel('Time')
plt.ylabel('Actual Stock Price')
plt.legend(loc='upper left', fontsize=8)
plt.show()
stock price prediction

Conclusion

Time Series forecasting is really useful when we have to take future decisions or we have to do analysis, we can quickly do that using ARIMA, there are lots of other Models from we can do the time series forecasting but ARIMA is really easy to understand.

I hope this article will help you and save a good amount of time. Let me know if you have any suggestions.

HAPPY CODING.

Prabhat Pathak (Linkedin profile) is a Senior Analyst and innovation Enthusiast.

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