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.
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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
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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.
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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.
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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
TECH_MA
HCL
INFOSYS
TCS
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
PNIES
HINDRA
WIPRO
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.
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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 figures7, 8, 9, 10 and 11 of the correlograms respectively.
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Figure 2: CORRLOGRAM OF HCL
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Figure 3 CORRELOGRAM OF INFOSYS
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Figure 4 CORRELOGRAM OF TCS
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Figure 5 CORRELOGRAM OFTECHMAHINDRA
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Figure 6 CORRELOGRAM OF WIPRO
Date: 09/18/18 Time: 22:38
Sample: 1 1236
Included observations: 1235
Autocorrelation
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Partial
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AC
Correlation
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1
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PAC Q-Stat Prob
0.007 0.007 0.0690 0.793
2 -0.096 -0.096 11.484 0.003
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3 -0.052 -0.051 14.845 0.002
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4
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5 -0.020 -0.030 15.587 0.008
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6 -0.010 -0.011 15.711 0.015
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7 -0.033 -0.037 17.051 0.017
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8
0.038 0.034 18.802 0.016
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9
0.038 0.031 20.597 0.015
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10 0.033 0.036 21.932 0.015
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11 -0.044 -0.034 24.296 0.012
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12 -0.037 -0.029 25.961 0.011
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13 0.002 -0.001 25.966 0.017
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14 -0.021 -0.032 26.543 0.022
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15 0.019 0.022 27.005 0.029
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16 0.034 0.029 28.420 0.028
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17 0.057 0.057 32.455 0.013
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18 0.014 0.016 32.691 0.018
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19 0.044 0.056 35.155 0.013
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20 -0.066 -0.055 40.621 0.004
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0.015 0.006 15.113 0.004
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21 -0.039 -0.025 42.549 0.004
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22 -0.021 -0.021 43.081 0.005
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23 -0.001 -0.014 43.082 0.007
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24 -0.033 -0.036 44.417 0.007
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25 0.069 0.058 50.516 0.002
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26 0.008 -0.005 50.589 0.003
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28 0.021 0.034 56.560 0.001
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29 -0.004 -0.014 56.582 0.002
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30 -0.023 -0.010 57.238 0.002
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31 -0.022 -0.017 57.830 0.002
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32 -0.034 -0.043 59.271 0.002
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33 0.011 -0.002 59.421 0.003
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34 0.059 0.036 63.894 0.001
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35 -0.027 -0.036 64.827 0.002
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36 -0.036 -0.025 66.460 0.001
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27 -0.065 -0.068 55.992 0.001
Figure 7 AFTER DIFFERENCING LINE GRAPH AND CORRLOGRAM OF HCL
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Date: 09/18/18 Time: 22:43
Sample: 1 1236
Included observations: 1235
Autocorrelation
Partial
AC
Correlation
PAC Q-Stat Prob
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1 -0.013 -0.013 0.2150 0.643
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2 -0.050 -0.050 3.2845 0.194
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3 -0.059 -0.061 7.6050 0.055
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4
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5 -0.016 -0.021 9.4505 0.092
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6 -0.013 -0.014 9.6526 0.140
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7 -0.029 -0.028 10.734 0.151
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8
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9 -0.003 -0.005 14.804 0.096
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10 0.018 0.021 15.201 0.125
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11 -0.005 0.003 15.238 0.172
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12 0.012 0.009 15.418 0.219
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13 -0.049 -0.046 18.478 0.140
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14 -0.039 -0.041 20.381 0.119
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15 0.019 0.018 20.843 0.142
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16 -0.005 -0.018 20.879 0.183
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17 0.039 0.041 22.788 0.156
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18 0.034 0.035 24.213 0.148
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19 0.058 0.060 28.452 0.075
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20 -0.024 -0.018 29.157 0.085
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21 -0.013 -0.003 29.372 0.105
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22 -0.023 -0.015 30.023 0.118
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23 -0.019 -0.026 30.460 0.137
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24 -0.039 -0.035 32.369 0.118
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25 0.045 0.039 34.970 0.089
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26 -0.034 -0.040 36.422 0.084
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27 -0.012 -0.026 36.616 0.102
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28 -0.038 -0.035 38.440 0.090
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29 0.004 -0.010 38.459 0.112
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30 -0.014 -0.014 38.708 0.132
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0.035 0.031 9.1450 0.058
0.057 0.052 14.794 0.063
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31 -0.042 -0.041 40.899 0.110
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32 -0.056 -0.045 44.811 0.066
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33 0.039 0.027 46.752 0.057
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34 0.012 0.002 46.937 0.069
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35 -0.009 -0.014 47.039 0.084
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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
Included observations: 1235
Autocorrelation
|
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*|
Partial
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AC
Correlation
|
*|
1
|
PAC Q-Stat Prob
0.007 0.007 0.0675 0.795
2 -0.067 -0.068 5.7092 0.058
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3 -0.047 -0.046 8.4038 0.038
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4
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5 -0.042 -0.048 11.171 0.048
*|
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*|
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0.022 0.019 9.0275 0.060
6 -0.074 -0.074 18.020 0.006
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7 -0.020 -0.024 18.511 0.010
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8
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9 -0.024 -0.034 22.825 0.007
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10 -0.016 -0.011 23.129 0.010
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11 -0.024 -0.029 23.841 0.013
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12 0.014 0.000 24.077 0.020
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13 0.001 -0.003 24.078 0.030
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14 -0.001 0.001 24.079 0.045
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15 -0.025 -0.028 24.874 0.052
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16 0.022 0.015 25.483 0.062
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17 0.002 -0.002 25.490 0.084
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18 0.007 0.007 25.549 0.111
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19 0.040 0.045 27.514 0.093
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20 0.020 0.016 28.020 0.109
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21 0.024 0.028 28.717 0.121
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22 -0.046 -0.040 31.433 0.088
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23 0.032 0.042 32.759 0.085
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24 -0.021 -0.023 33.295 0.098
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25 0.035 0.046 34.876 0.090
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26 -0.033 -0.027 36.260 0.087
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27 0.014 0.016 36.504 0.105
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28 0.036 0.036 38.144 0.096
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29 0.004 0.004 38.165 0.119
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30 -0.030 -0.014 39.279 0.120
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31 -0.040 -0.039 41.318 0.102
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32 0.018 0.019 41.720 0.117
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33 0.008 -0.003 41.795 0.140
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34 -0.001 0.014 41.796 0.168
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35 -0.006 -0.008 41.834 0.198
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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
Included observations: 1235
Autocorrelation
|
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*|
Partial
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AC
PAC Q-Stat Prob
1
0.046
0.046 2.6646 0.103
2
-0.072
-0.075 9.1618 0.010
Correlation
|
*|
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3
0.007
0.015 9.2314 0.026
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4
0.030
0.024 10.368 0.035
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5
0.053
0.053 13.907 0.016
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6
-0.058
-0.060 18.145 0.006
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7
-0.011
0.002 18.289 0.011
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8
0.000
-0.010 18.289 0.019
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9
0.052
0.052 21.703 0.010
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10
0.015
0.009 21.977 0.015
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11
-0.040
-0.028 23.996 0.013
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12
0.040
0.041 25.972 0.011
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13
0.030
0.019 27.113 0.012
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14
0.038
0.037 28.928 0.011
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15
0.015
0.019 29.192 0.015
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16
-0.032
-0.026 30.460 0.016
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17
0.033
0.029 31.826 0.016
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18
-0.017
-0.027 32.194 0.021
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19
-0.001
0.004 32.195 0.030
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20
-0.045
-0.043 34.738 0.022
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21
-0.014
-0.008 35.002 0.028
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22
-0.010
-0.025 35.118 0.038
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23
0.040
0.047 37.120 0.032
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24
0.006
-0.005 37.171 0.042
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25
0.035
0.051 38.699 0.039
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26
-0.043
-0.058 40.997 0.031
|
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27
-0.008
-0.001 41.087 0.040
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28
0.065
0.054 46.380 0.016
|
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29
-0.035
-0.039 47.924 0.015
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30
-0.063
-0.050 52.921 0.006
|
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31
-0.068
-0.063 58.831 0.002
*|
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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
Included observations: 1235
Autocorrelation
Partial
AC
Correlation
PAC Q-Stat Prob
|
|
|
|
1 -0.043 -0.043 2.2705 0.132
|
|
|
|
2
|
|
|
|
3 -0.029 -0.028 3.4832 0.323
|
|
|
|
4 -0.045 -0.048 6.0481 0.196
|
|
|
|
5
|
|
|
|
6 -0.030 -0.026 9.9355 0.127
|
|
|
|
7
|
|
|
|
8 -0.052 -0.049 14.077 0.080
|
|
|
|
9
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0.012 0.010 2.4551 0.293
0.047 0.044 8.8482 0.115
0.025 0.020 10.738 0.150
0.041 0.040 16.183 0.063
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|
|
|
|
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
|
|
|
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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
|
|
|
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25 0.024 0.025 29.338 0.250
|
|
|
|
26 -0.000 0.001 29.338 0.296
|
|
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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
|
|
|
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32 0.035 0.014 41.727 0.117
|
|
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33 -0.017 -0.004 42.099 0.133
|
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34 -0.013 -0.020 42.322 0.155
|
|
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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.
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Table 2 HCL
Adjusted R2 SE of Regression
ARIMA
AIC
(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
Adjusted R2 S.E of Regression
ARIMA
AIC
(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
Adjusted
S.E of
R2
Regression
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
ARIMA
AIC
(1,0,0)
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(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
Adjusted R2 S.E of Regression
ARIMA
AIC
(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
Adjusted
S.E of
R2
Regression
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
ARIMA
AIC
(1,0,0)
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
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Analysis of Daily Stock Trend Prediction using Arima Model
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.
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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
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Analysis of Daily Stock Trend Prediction using Arima Model
Figure 15 FORECAST GRAPH of TCS
Figure 16 FORECAST GRAPH of TECH_MAHINDRA
320
Forecast: WIPROF
Actual: WIPRO
Forecast sample: 1 1236
Adjusted sample: 2 1236
Included observations: 1235
Root Mean Squared Error
Mean Absolute Error
Mean Abs. Percent Error
Theil Inequality Coefficient
Bias Proportion
Variance Proportion
Covariance Proportion
280
240
200
160
120
80
33.05783
26.44685
20.67012
0.098720
0.005134
0.427214
0.567652
2007-03-01
19-03-2007
2007-01-06
2007-10-08
23-10-2007
2008-03-01
14-03-2008
2008-02-06
2008-11-08
24-10-2008
2009-12-01
30-03-2009
16-06-2009
25-08-2009
2009-10-11
22-01-2010
2010-08-04
18-06-2010
27-08-2010
2010-08-11
19-01-2011
2011-01-04
15-06-2011
25-08-2011
2011-11-11
40
WIPROF
± 2 S.E.
Figure 17 FORECAST GRAPH of WIPRO
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Mohankumari C, Vishukumar M and Nagaraja Rao Chillale
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
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
TECHMAHINDRA WIPRO
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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