analysis of daily stock trend prediction …...model, elaborates the process of building stock trend...

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International Journal of Mechanical Engineering and Technology (IJMET)

Volume 10, Issue 01, January 2019, pp. 1772-1792, Article ID: IJMET_10_01_176

Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=1

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

ANALYSIS OF DAILY STOCK TREND

PREDICTION USING ARIMA MODEL

Mohankumari C

Department of Statistics, REVA University,

Vishukumar M

Department of Mathematics, REVA University,

Nagaraja Rao Chillale

Department of Statistics, Bangalore University,

Bangalore, Karnataka, India

ABSTRACT

In literature of time series prediction the autoregressive integrated moving

average(ARIMA) models have been explained clearly. This paper using the ARIMA

model, elaborates the process of building stock trend predictive model. Published

data of stock price obtained from National Stock Exchange (NSE) during the period

from Jan-2007 to Dec-2011. The results obtained revealed that for short-term

prediction the ARIMA model which has a strong prospects and for stock price

prediction even it can be positively compete with existing techniques.

Keywords: ARIMA , Stock rate, Short-term prediction, Forecast.

Cite this Article: Mohankumari C, Vishukumar M and Nagaraja Rao Chillale,

Analysis of Daily Stock Trend Prediction using Arima Model, International Journal

of Mechanical Engineering and Technology, 10(1), 2019, pp. 1772-1792.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=1

1. INTRODUCTION

A stock is known as equity of share, it is a portion of the ownership in a corporate sector by

an individual. Hence, a stock of a company entitles its holder a share in its profit. Issuing

shares a corporate company can mobilize huge capitals. The stock market is a field of

financial game and it can fetch bigger financial benefits compared to fixed deposits with

banks and for other such investments. The stability as well as the inflation of the economy of

a country is swiftly and better reflected by the trend in the stock market. So the study of the

fluctuations in the stock market becomes important. There are many approaches to know the

depth of an analysis of stock price variation.

Mohankumari C, Vishukumar M and Nagaraja Rao Chillale


Forecasting is a necessity of human life and a common problem in all branches of

learning. Financial and economic problems are domains in which forecasting is of major

importance.

Stock market analysts have adopted many statistical techniques likes Auto Regressive

Moving Average (ARMA) , Auto Regressive Integrated Moving Average (ARIMA), Auto

Regressive Conditional Heteroscedasticity (ARCH),Generalized Auto Regressive Conditional

Heteroscadasticity (GARCH), ARMA-EGARCH , Box and Jenkins approach along with

various soft computing and evolutionary computing methods.

An interesting area of research is Prediction, it will continue to be making researchers in

the realm field and also desires to improve existing predictive models. In the stock market we

focus on the real world problem.

1.1. Literature survey

Uma Devi and et.al[2] explains the seasonal trend and flow is the highlight of the

stock market. Eventually investors as well as the stock broking company will also

observe and capture the variations, as constant growth of the index. This will help new

investor as well as existing ones to make a strategic decision. It can be achieved by

experience and the constant observation by the investors. In order to overcome the

above said issues, ARIMA algorithm has been suggested in three steps, Step 1: Model

identification , Step 2: Model estimation and Step 3: Forecasting.

Ayodele Adebiyi, A and et.al[1] , Uma Devi, B and et.al [2] Pai, P and et.al[3] Wang,

J.J and et.al [4] and Wei, L.Y[5] authors explains to execute in financial forecasting

due to complex nature of stock market Stock price prediction is regarded as one of the

most difficult task.

Atsalakis, G.S and et.al[6] explained in this paper as to catch hold of any forecasting

method is the desire of many investors which would give assurance of easy profit and

minimize investment risk from the stock market. For researchers to develop gradually

new predictive models remains a motivating factor.

Mitra, S.K[7] , Atsalakis, G.S and et.al[8] , Mohamed, M.M[9] authors asserted as in

the past years, to predict stock prices several models and techniques had been

developed. One of them is: an artificial neural networks (ANNs) model due to its

ability to learn patterns from data and infer solution from unknown data are very

popular. Few related works on ANNs model are given in their literature for stock price

prediction.

Wang, J.J and et.al[4] defined in recent time, to improve stock price predictive models

by exploiting the unique strength hybrid approaches have also been engaged. ANNs is

from artificial intelligence perspectives. From statistical models perspective ARIMA

models have been derived. Generally, from two perspectives: statistical and artificial

intelligence techniques the prediction can be done it is reported in their literature.

Merh, N and et.al[10] , Sterba, J and et.al[11] and Javier, C and et.al[12] defined as in

financial time series forecasting, ARIMA models are known to be robust and efficient,

especially for short-term prediction than the popular ANNs techniques. In fields of

Economics and Finance they have been extensively used. Other statistical models like:

regression method, exponential smoothing, generalized autoregressive and conditional

heteroskedasticity (GARCH) are also discussed.

Few related works for forecasting using ARIMA model also been discussed by [13,

14, 15, 16, 17, 18] also.

Analysis of Daily Stock Trend Prediction using Arima Model


For our proposed research, extensive process of building ARIMA models for short-term

stock price prediction is presented. The results obtained from real-life data demonstrated the

potential strength of ARIMA models to provide investors short-term prediction that could aid

investment decision making process. The rest of the paper is organized as follows: Section-2

presents brief overview of ARIMA model. Section-3 describes the methods (methodology)

used, while section-4 discusses the experimental results obtained. The paper is concluded in

section-5 with observations.

2. ARIMA MODEL

The general model introduced by Box and Jenkins (1976) includes AR (autoregressive) as

well as MA(moving average) parameters includes I(differencing) in the formulation of the

model[Text book]. It also referred to as Box-Jenkins methods composed of set of activities for

identifying, estimating and diagnosing ARIMA models with time series data[20]. The model

is most prominent methods in financial forecasting [3, 14, 11]. ARIMA models have shown

efficient capability to generate short-term forecasts. It constantly outperformed complex

structural models in short-term prediction [19]. In ARIMA model, the future value of a

variable is a linear combination of past values and past errors, expressed as follows:

Yt = μ or ϕ0 + ϕ1 Yt-1 + ϕ2 Yt-2 +...+ ϕpYt-p + Ɛt - θ1 Ɛt-1 - θ2 Ɛt-2 -...- θq Ɛt-q .(1)

where, Yt is the actual value, μ or ϕ0 is a constant, εt is the random error at t, ϕi and θj are

the coefficients of p and q which are integers that are often referred to as autoregressive and

moving average parameters, respectively.

3. METHODS

The method to develop ARIMA model for stock price forecasting is used in this study is

explained in detail in the subsections below. The tool, used for implementation is R-Software

and Eviews software version 8.1. Stock data used in this research work are historical daily

stock prices, obtained from five companies. The data is composed of four elements, namely:

open price, low price, high price and close price respectively. In this research the closing

price is chosen to represent the price of the index for prediction. Closing price is chosen

because in a trading day it reflects all the activities of the index.

Among several experiments performed to regulate the best ARIMA model, in this study the

following criteria are used for stock index.

i. Relatively small AIC (Akaike Information Criterion) or BIC (Bayesian or Schwarz

Information Criterion)

ii. Relatively small standard error of regression (S.E. of regression)

iii. Relatively high of adjusted R2.

iv. Q-statistics and Correlogram show that there is no significant pattern left in the

autocorrelation functions (ACFs) and partial autocorrelation functions (PACFs) of the

residuals, it means the residual of the selected model are white noise.

The ARIMA model-development process is described in below subsections.

3.1. Descriptive Statistics of the Stock Index

NSE stock data is used in this study covers the period from 2nd

January, 2007 to 30th

December, 2011 having a total number of 1236 observations. Table-1 represents the summary

statistics of 5 companies. Serving to discover tests for normality is to run descriptive statistics

to get Skewness and Kurtosis.



Skewness is the tilt (or lack of it) in a distribution. The more common type is right skew,

where the smaller tail points to the right. Less common is left skew, where the smaller tail is

points left. Skew should be within +1 to -1 range when the data are normally distributed. We

observed that Skewness for the daily returns of all the stocks are within +1 to -1, which is an

indication that the data are normally distributed.

Kurtosis is the peakedness of a distribution (i.e., kurtosis should be within +3 to -3 range

when the data are normally distributed). From the table-1, we observe that kurtosis of

TECHMAHINDRA has high kurtosis(>3) which is an indication that data are not normally

distributed. But we assume in the long run the variables are normally distributed.

Table 1 SUMMARY STATISTICS of Daily data of companies HCL, INFOSYS, TCS,

TECHMAHINDRA and WIPRO

INDEX/COM

PNIES HCL INFOSYS TCS

TECH_MA

HINDRA WIPRO

Observations 1236 1236 1236 1236 1236

Mean 161.2614 549.6627 680.3454 208.1490 164.4384

Median 164.2650 541.1700 617.6000 186.7550 168.0400

Maximum 261.4300 870.3700 1239.850 495.2000 245.6800

Minimum 44.85000 275.5800 223.1000 52.33000 60.27000

Std. Dev. 52.78538 150.7456 292.7018 87.24827 46.59308

Skewness -0.304600 0.044723 0.341765 0.691708 -0.462491

Kurtosis 2.520548 1.860538 1.906683 3.323833 2.359956

3.2. An ARIMA (p, d, q) Model for Stock Index

3.2.1. Model Identification

Figure- 1 renders (reproduce) to have general overview of the original pattern whether the

time series is stationary or not. From the figure-1 we can see the time series have random

walk pattern.



Figure 1 Graphical representation of the Stock closing price of HCL, INFOSYS, TCS,

TECH_MAHINDRA, WIPRO

3.2.2. Model Estimation

Figures- 2, 3, 4, 5, 6 are the correlograms of HCL, INFOSYS, TCS TECHMAHINDRA

and WIPRO. From the graphs, the time series is seems to be non-stationary, since the ACF

dies down extremely slowly. "If the series is not stationary, it is converted to a stationary

series by differencing [lag]". After the first difference (D), the differencing series of HCL,

INFOSYS, TCS, TECHMAHINDRA and WIPRO becomes stationary as shown in figures-

7, 8, 9, 10 and 11 of the correlograms respectively.



Figure 2: CORRLOGRAM OF HCL Figure 3 CORRELOGRAM OF INFOSYS



Figure 4 CORRELOGRAM OF TCS Figure 5 CORRELOGRAM OFTECHMAHINDRA



Figure 6 CORRELOGRAM OF WIPRO

Date: 09/18/18 Time: 22:38

Sample: 1 1236

Included observations: 1235

Autocorrelation Partial

Correlation AC PAC Q-Stat Prob

| | | | 1 0.007 0.007 0.0690 0.793

*| | *| | 2 -0.096 -0.096 11.484 0.003



| | | | 3 -0.052 -0.051 14.845 0.002

| | | | 4 0.015 0.006 15.113 0.004

| | | | 5 -0.020 -0.030 15.587 0.008

| | | | 6 -0.010 -0.011 15.711 0.015

| | | | 7 -0.033 -0.037 17.051 0.017

| | | | 8 0.038 0.034 18.802 0.016

| | | | 9 0.038 0.031 20.597 0.015

| | | | 10 0.033 0.036 21.932 0.015

| | | | 11 -0.044 -0.034 24.296 0.012

| | | | 12 -0.037 -0.029 25.961 0.011

| | | | 13 0.002 -0.001 25.966 0.017

| | | | 14 -0.021 -0.032 26.543 0.022

| | | | 15 0.019 0.022 27.005 0.029

| | | | 16 0.034 0.029 28.420 0.028

| | | | 17 0.057 0.057 32.455 0.013

| | | | 18 0.014 0.016 32.691 0.018

| | | | 19 0.044 0.056 35.155 0.013

*| | | | 20 -0.066 -0.055 40.621 0.004

| | | | 21 -0.039 -0.025 42.549 0.004

| | | | 22 -0.021 -0.021 43.081 0.005

| | | | 23 -0.001 -0.014 43.082 0.007

| | | | 24 -0.033 -0.036 44.417 0.007

| | | | 25 0.069 0.058 50.516 0.002

| | | | 26 0.008 -0.005 50.589 0.003

| | *| | 27 -0.065 -0.068 55.992 0.001

| | | | 28 0.021 0.034 56.560 0.001

| | | | 29 -0.004 -0.014 56.582 0.002

| | | | 30 -0.023 -0.010 57.238 0.002

| | | | 31 -0.022 -0.017 57.830 0.002

| | | | 32 -0.034 -0.043 59.271 0.002

| | | | 33 0.011 -0.002 59.421 0.003

| | | | 34 0.059 0.036 63.894 0.001

| | | | 35 -0.027 -0.036 64.827 0.002

| | | | 36 -0.036 -0.025 66.460 0.001

Figure 7 AFTER DIFFERENCING LINE GRAPH AND CORRLOGRAM OF HCL



Date: 09/18/18 Time: 22:43

Sample: 1 1236




| | | | 1 -0.013 -0.013 0.2150 0.643

| | | | 2 -0.050 -0.050 3.2845 0.194

| | | | 3 -0.059 -0.061 7.6050 0.055

| | | | 4 0.035 0.031 9.1450 0.058

| | | | 5 -0.016 -0.021 9.4505 0.092

| | | | 6 -0.013 -0.014 9.6526 0.140

| | | | 7 -0.029 -0.028 10.734 0.151

| | | | 8 0.057 0.052 14.794 0.063

| | | | 9 -0.003 -0.005 14.804 0.096

| | | | 10 0.018 0.021 15.201 0.125

| | | | 11 -0.005 0.003 15.238 0.172

| | | | 12 0.012 0.009 15.418 0.219

| | | | 13 -0.049 -0.046 18.478 0.140

| | | | 14 -0.039 -0.041 20.381 0.119

| | | | 15 0.019 0.018 20.843 0.142

| | | | 16 -0.005 -0.018 20.879 0.183

| | | | 17 0.039 0.041 22.788 0.156

| | | | 18 0.034 0.035 24.213 0.148

| | | | 19 0.058 0.060 28.452 0.075

| | | | 20 -0.024 -0.018 29.157 0.085

| | | | 21 -0.013 -0.003 29.372 0.105

| | | | 22 -0.023 -0.015 30.023 0.118

| | | | 23 -0.019 -0.026 30.460 0.137

| | | | 24 -0.039 -0.035 32.369 0.118

| | | | 25 0.045 0.039 34.970 0.089

| | | | 26 -0.034 -0.040 36.422 0.084

| | | | 27 -0.012 -0.026 36.616 0.102

| | | | 28 -0.038 -0.035 38.440 0.090

| | | | 29 0.004 -0.010 38.459 0.112

| | | | 30 -0.014 -0.014 38.708 0.132



| | | | 31 -0.042 -0.041 40.899 0.110

| | | | 32 -0.056 -0.045 44.811 0.066

| | | | 33 0.039 0.027 46.752 0.057

| | | | 34 0.012 0.002 46.937 0.069

| | | | 35 -0.009 -0.014 47.039 0.084

| | | | 36 -0.039 -0.038 49.017 0.073

Figure 8 AFTER DIFFERENCING CORRLOGRAM OF INFOSYS

Date: 09/18/18 Time: 22:46

Sample: 1 1236




| | | | 1 0.007 0.007 0.0675 0.795

*| | *| | 2 -0.067 -0.068 5.7092 0.058

| | | | 3 -0.047 -0.046 8.4038 0.038

| | | | 4 0.022 0.019 9.0275 0.060

| | | | 5 -0.042 -0.048 11.171 0.048

*| | *| | 6 -0.074 -0.074 18.020 0.006

| | | | 7 -0.020 -0.024 18.511 0.010

| | | | 8 0.054 0.040 22.092 0.005

| | | | 9 -0.024 -0.034 22.825 0.007

| | | | 10 -0.016 -0.011 23.129 0.010

| | | | 11 -0.024 -0.029 23.841 0.013

| | | | 12 0.014 0.000 24.077 0.020

| | | | 13 0.001 -0.003 24.078 0.030

| | | | 14 -0.001 0.001 24.079 0.045

| | | | 15 -0.025 -0.028 24.874 0.052

| | | | 16 0.022 0.015 25.483 0.062

| | | | 17 0.002 -0.002 25.490 0.084

| | | | 18 0.007 0.007 25.549 0.111

| | | | 19 0.040 0.045 27.514 0.093

| | | | 20 0.020 0.016 28.020 0.109

| | | | 21 0.024 0.028 28.717 0.121

| | | | 22 -0.046 -0.040 31.433 0.088

| | | | 23 0.032 0.042 32.759 0.085



| | | | 24 -0.021 -0.023 33.295 0.098

| | | | 25 0.035 0.046 34.876 0.090

| | | | 26 -0.033 -0.027 36.260 0.087

| | | | 27 0.014 0.016 36.504 0.105

| | | | 28 0.036 0.036 38.144 0.096

| | | | 29 0.004 0.004 38.165 0.119

| | | | 30 -0.030 -0.014 39.279 0.120

| | | | 31 -0.040 -0.039 41.318 0.102

| | | | 32 0.018 0.019 41.720 0.117

| | | | 33 0.008 -0.003 41.795 0.140

| | | | 34 -0.001 0.014 41.796 0.168

| | | | 35 -0.006 -0.008 41.834 0.198

| | | | 36 0.024 0.020 42.585 0.209

Figure 9 AFTER DIFFERENCING CORRLOGRAM OF TCS

Date: 09/18/18 Time: 22:49

Sample: 1 1236




| | | | 1 0.046 0.046 2.6646 0.103

*| | *| | 2 -0.072 -0.075 9.1618 0.010

| | | | 3 0.007 0.015 9.2314 0.026

| | | | 4 0.030 0.024 10.368 0.035

| | | | 5 0.053 0.053 13.907 0.016

| | | | 6 -0.058 -0.060 18.145 0.006

| | | | 7 -0.011 0.002 18.289 0.011

| | | | 8 0.000 -0.010 18.289 0.019

| | | | 9 0.052 0.052 21.703 0.010

| | | | 10 0.015 0.009 21.977 0.015

| | | | 11 -0.040 -0.028 23.996 0.013

| | | | 12 0.040 0.041 25.972 0.011

| | | | 13 0.030 0.019 27.113 0.012

| | | | 14 0.038 0.037 28.928 0.011

| | | | 15 0.015 0.019 29.192 0.015

| | | | 16 -0.032 -0.026 30.460 0.016



| | | | 17 0.033 0.029 31.826 0.016

| | | | 18 -0.017 -0.027 32.194 0.021

| | | | 19 -0.001 0.004 32.195 0.030

| | | | 20 -0.045 -0.043 34.738 0.022

| | | | 21 -0.014 -0.008 35.002 0.028

| | | | 22 -0.010 -0.025 35.118 0.038

| | | | 23 0.040 0.047 37.120 0.032

| | | | 24 0.006 -0.005 37.171 0.042

| | | | 25 0.035 0.051 38.699 0.039

| | | | 26 -0.043 -0.058 40.997 0.031

| | | | 27 -0.008 -0.001 41.087 0.040

| | | | 28 0.065 0.054 46.380 0.016

| | | | 29 -0.035 -0.039 47.924 0.015

| | | | 30 -0.063 -0.050 52.921 0.006

*| | | | 31 -0.068 -0.063 58.831 0.002

| | | | 32 0.025 0.018 59.651 0.002

| | | | 33 -0.000 -0.012 59.651 0.003

| | | | 34 -0.060 -0.043 64.187 0.001

| | | | 35 -0.019 -0.007 64.649 0.002

| | | | 36 -0.001 -0.006 64.652 0.002

Figure 10 After Differencing Corrlogram Of Tech_Mahindra

Date: 09/18/18 Time: 22:50

Sample: 1 1236




| | | | 1 -0.043 -0.043 2.2705 0.132

| | | | 2 0.012 0.010 2.4551 0.293

| | | | 3 -0.029 -0.028 3.4832 0.323

| | | | 4 -0.045 -0.048 6.0481 0.196

| | | | 5 0.047 0.044 8.8482 0.115

| | | | 6 -0.030 -0.026 9.9355 0.127

| | | | 7 0.025 0.020 10.738 0.150

| | | | 8 -0.052 -0.049 14.077 0.080

| | | | 9 0.041 0.040 16.183 0.063



| | | | 10 0.032 0.033 17.473 0.065

| | | | 11 -0.030 -0.027 18.564 0.069

| | | | 12 0.008 0.001 18.654 0.097

| | | | 13 0.023 0.036 19.326 0.113

| | | | 14 0.006 0.003 19.371 0.151

| | | | 15 0.006 0.004 19.412 0.196

| | | | 16 0.013 0.016 19.639 0.237

| | | | 17 0.031 0.036 20.830 0.234

| | | | 18 0.018 0.022 21.237 0.268

| | | | 19 0.018 0.015 21.623 0.303

| | | | 20 -0.030 -0.026 22.784 0.300

| | | | 21 -0.028 -0.023 23.745 0.306

| | | | 22 0.031 0.028 24.987 0.298

| | | | 23 -0.033 -0.034 26.394 0.283

| | | | 24 -0.042 -0.050 28.630 0.234

| | | | 25 0.024 0.025 29.338 0.250

| | | | 26 -0.000 0.001 29.338 0.296

| | | | 27 0.039 0.028 31.225 0.262

| | | | 28 -0.025 -0.025 32.038 0.273

| | | | 29 -0.040 -0.041 34.061 0.237

| | | | 30 -0.005 -0.003 34.094 0.277

*| | *| | 31 -0.069 -0.074 40.203 0.125

| | | | 32 0.035 0.014 41.727 0.117

| | | | 33 -0.017 -0.004 42.099 0.133

| | | | 34 -0.013 -0.020 42.322 0.155

| | | | 35 0.027 0.018 43.229 0.160

| | | | 36 -0.023 -0.015 43.915 0.171

Figure 11 After Differencing Corrlogram Of Wipro

3.2.3. Model Checking

The model checking done with Augmented Dickey Fuller (ADF) unit root test based on “First

Differencing (D)” of NSE stock index. After the first-difference of the series the result

confirms that the series becomes stationary.



Table 2 HCL

ARIMA AIC Adjusted R2 SE of Regression

(1,0,0) 5.6894 0.9938 4.1561

(1,0,1) 5.6909 0.9938 4.1576

(2,0,0) 6.3879 0.9876 5.8932

(0,0,1) 9.0987 0.8125 22.8564

(0,0,2) 9.1691 0.7988 23.6750

(1,1,0) 5.6929 -0.0015 4.1632

(0,1,0) 5.6906 -0.0007 4.1602

(0,1,1) 5.6922 -0.0014 4.1617

(1,1,2) 5.6854 0.0068 4.1460

(2,1,0) 5.6841 0.0077 4.1449

(2,1,2) 5.6857 0.0069 4.1465

Table 3 INFOSYS

ARIMA AIC Adjusted R2 S.E of Regression

(1,0,0) 7.6061 0.9948 10.8365

(1,0,1) 7.6076 0.9948 10.8402

(2,0,0) 8.2821 0.9899 15.1940

(0,0,1) 10.9483 0.8539 57.6277

(0,0,2) 11.0119 0.8443 59.4886

(1,1,0) 7.6098 -0.0009 10.8563

(0,1,0) 7.6082 -0.0004 10.8522

(0,1,1) 7.6096 -0.0009 10.8555

(1,1,2) 7.6089 0.0007 10.8473

(2,1,0) 7.6080 -0.0014 10.8466

(2,1,2) 7.6079 0.0023 10.8416

Table 4 TCS

ARIMA AIC Adjusted

R2

S.E of

Regression

(1,0,0) 8.2270 0.9975 14.7814

(1,0,1) 8.2286 0.9975 14.7868

(2,0,0) 8.9249 0.9949 20.9539

(0,0,1) 12.0787 0.8795 101.4145

(0,0,2) 12.1528 0.8707 105.2405



(1,1,0) 8.2279 0.0002 14.7879

(0,1,0) 8.2265 0.0008 14.7836

(0,1,1) 8.2281 0.000039 14.7894

(1,1,2) 8.2249 0.0040 14.7593

(2,1,0) 8.2236 0.0049 14.7559

(2,1,2) 8.2201 0.0091 14.7242

Table 5 TECHMAHINDRA

ARIMA AIC Adjusted R2 S.E of Regression

(1,0,0) 6.5663 0.9945 6.4432

(1,0,1) 6.5652 0.9945 6.4369

(2,0,0) 7.3021 0.9885 9.3083

(0,0,1) 10.1093 0.8114 37.8831

(0,0,2) 10.2066 0.7922 39.7791

(1,1,0) 6.5674 0.0014 6.4467

(0,1,0) 6.5671 0.0002 6.4482

(0,1,1) 6.5662 0.0018 6.4429

(1,1,2) 6.5635 0.0062 6.4312

(2,1,0) 6.5644 0.0047 6.4369

(2,1,2) 6.5499 0.0198 6.3877

Table 6 WIPRO

ARIMA AIC Adjusted

R2

S.E of

Regression

(1,0,0) 5.3961 0.9941 3.5872

(1,0,1) 5.3950 0.9941 3.5857

(2,0,0) 6.0418 0.9987 4.9567

(0,0,1) 8.9007 0.8026 20.7018

(0,0,2) 8.9336 0.7959 21.0452

(1,1,0) 5.3964 0.0007 3.5896

(0,1,0) 5.3963 -0.0003 3.5908

(0,1,1) 5.3961 0.0006 3.5890

(1,1,2) 5.3979 0.00003 3.5909

(2,1,0) 5.3979 -0.00106 3.5924

(2,1,2) 5.3987 -0.0010 3.5922

Table-2, 3, 4, 5 and 6 shows the different parameters of autoregressive(p), moving

average(q) and differncing(d) among the several ARIMA model experimented upon



companies such as HCL, INFOSYS, TCS, TECHMAHINDRA and WIPRO. Among the

various ARIMA models: ARIMA (2, 1, 0) is considered the best for HCL, ARIMA(1,0,0) is

considered the best for INFOSYS, ARIMA(2,1,2) is considered the best for TCS,

ARIMA(2,1,2) is considered the best for TECHMAHINDRA and ARIMA(1,0,1) is

considered the best for WIPRO. The model contains the smallest Akaike information

criterion(AIC) and relatively smallest standard error(SE) of regression.

Figure 12 Correlogram of Residuals

Figure-12 represents the correlogram of residuals of the series. If the model is good, the

random errors will be residuals of the series. Since there are no significant spikes of ACFs

and PACFs, which means that are white noise of the residuals of the selected ARIMA models,

in the time series no other significant patterns are left. Therefore, there is no need to consider

any AR(p) and MA(q) further.

The bold and coloured row represents among the several experiments are the best

ARIMA model as shown in tables- 2, 3, 4, 5 and 6.



4. RESULTS AND DISCUSSIONS

In the below section the experimental results of each of stock index are discussed.

4.1. Result for NSE Stock Price Prediction of companies such as HCL, INFOSYS,

TCS, TECHMAHINDRA and WIPRO of ARIMA Model

The graphical illustration to see the performance of the ARIMA model selected by the level of

accuracy of the predicted price against actual stock price. It is obvious that the performance is

come to be satisfactory from the graphs.

4.2. Discussion

Figures-13, 14, 15, 16 and 17 explains that the values are minimal and the performance is

satisfactory can be seen from the graph.

Figure 13 FORECAST GRAPH of HCL

Figure 14 FORECAST GRAPH of INFOSYS



Figure 15 FORECAST GRAPH of TCS

Figure 16 FORECAST GRAPH of TECH_MAHINDRA

40

80

120

160

200

240

280

320

2007-0

3-0

1

19-0

3-2

007

2007-0

1-0

6

2007-1

0-0

8

23-1

0-2

007

2008-0

3-0

1

14-0

3-2

008

2008-0

2-0

6

2008-1

1-0

8

24-1

0-2

008

2009-1

2-0

1

30-0

3-2

009

16-0

6-2

009

25-0

8-2

009

2009-1

0-1

1

22-0

1-2

010

2010-0

8-0

4

18-0

6-2

010

27-0

8-2

010

2010-0

8-1

1

19-0

1-2

011

2011-0

1-0

4

15-0

6-2

011

25-0

8-2

011

2011-1

1-1

1

WIPROF ± 2 S.E.

Forecast: WIPROF

Actual: WIPRO

Forecast sample: 1 1236

Adjusted sample: 2 1236


Root Mean Squared Error 33.05783

Mean Absolute Error 26.44685

Mean Abs. Percent Error 20.67012

Theil Inequality Coefficient 0.098720

Bias Proportion 0.005134

Variance Proportion 0.427214

Covariance Proportion 0.567652

Figure 17 FORECAST GRAPH of WIPRO



Among the various ARIMA models: (2, 1, 0) is considered the best for HCL, (1,0,0) is

considered the best for INFOSYS, (2,1,2) is considered the best for TCS, (2,1,2) is considered

the best for TECHMAHINDRA and (1,0,1) is considered the best for WIPRO.

Companies→Index↓ HCL INFOSYS TCS TECHMAHINDRA WIPRO

RMSE 37.2189 88.2364 128.3115 54.4238 33.0578

MAE 29.2033 71.9108 101.7401 40.7803 26.4469

MAPE 26.8530 14.6673 22.0895 31.9529 20.6701

Variance 0.4965 0.3155 0.2171 0.2237 0.4272

Table 7 Forecasting measures of companies

From the table-7 we can see the forecast index among the various companies.

Based on the discussion of forecasting we can write the best models for companies HCL,

INFOSYS, TCS, TECHMAHINDRA and WIPRO such as:

Yt (HCL) = 9070.759 + 0.0079ϕ1Yt-1 - 0.0961ϕ2Yt-2 + Ɛt

Yt(INFOSYS) = 25742157 + 0.9935ϕ1Yt-1 + Ɛt

Yt(TCS) = 146514.3 + 0.6438ϕ1Yt-1 - 0.8654ϕ2Yt-2 + Ɛt + 0.6418θ1Ɛt-1 -0.8156θ2Ɛt-2

Yt(TECHMAHINDRA) = 49287.12 - 0.0145ϕ1Yt-1 - 0.9365ϕ2Yt-2 + Ɛt - 0.0464θ1Ɛt-1 - 0.9292θ2Ɛt-2

Yt (WIPRO) = 6189936.0 + 0.9951ϕ1Yt-1 + Ɛt + 0.0402θ1Ɛt-1

where, Ɛt = Yt - Yt^ (i.e., the difference between the actual value(Yt) of the series and the

forecasted value(Yt^)), ϕi and θj are the coefficients of p and q which are integers that are

often referred to as autoregressive and moving average parameters, respectively.

5. CONCLUSION

This paper presents for stock price prediction extensive process of building is an ARIMA

model. Based on historical data Forecasting with ARIMA provides a prediction, in which data

has been applied by first order difference to remove random walk pattern problems. The

experimental results on short-term basis are obtained with the best ARIMA model to predict

stock prices satisfactory. In stock market this could guide investors to make profitable

investment decisions. With the results obtained, the ARIMA models with emerging

forecasting techniques can compete reasonably well in short-term prediction. From the

analysis the different investors can choose companies according to their returns.

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