MODELING OF AUTOREGRESSIVE MOVING AVERAGE AND VECTOR AUTOREGRESSIVE FOR FORECASTING STOCK PRICE INDEX IN ASEAN COUNTRIES

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 9, Issue 11, November 2018, pp. 309–319, Article ID: IJMET_09_11_031
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=9&IType=11
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
MODELING OF AUTOREGRESSIVE MOVING
AVERAGE AND VECTOR AUTOREGRESSIVE
FOR FORECASTING STOCK PRICE INDEX IN
ASEAN COUNTRIES
Agus Suharsono
Department of Statistics, FMKSD, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia
Imam Safawi Ahmad
Department of Statistics, FMKSD, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia
Aryo Wibisono
Faculty of Economics, Wiraraja University, Sumenep, Indonesia.
Wara Pramesti
Faculty of Mathematics and Natural Science, Adi Buana University, Surabaya, Indonesia.
ABSTRACT
A country's stock price index is an important part to see, because it shows the
country's indicators of high or low economic growth or development. A country is said to
have a high economic growth rate if the country's stock price index increases every day.
One way of making decisions for short-term investments is the need for modeling to
forecast stock prices in the future period. In this research, modeling of share price of
Indonesia with ASEAN countries (Association of South East Asia Nations) including
developed and developing countries such as Malaysia, Singapore, Thailand, Philippines.
These countries are the founders of ASEAN and have a good stock price index. The
Indonesian stock price index (IDX, Indonesia Stock Exchange), Malaysia (KLCI, Kuala
Lumpur Composite Index), Singapore (SGX, Singapore Exchange), Thailand (SETI), Thai
Stock Exchange) and the Philippines (PSE, Philippine Stock Exchange) will affect each
other one another. For this we need a model that is suitable for the case above, namely
the pattern of relations between the country's stock price index. By using the ARIMA
method (Autoregressive Moving Average) and VAR (Vector Autoregressive) the best
model is obtained for the ASEAN stock price index. By using MAPE (Mean Absolute
Percentage Error), the results for the best model data in ARIMA are obtained, except for
Thailand, the best model is VAR. As for the sample data, the best model ARIMA was
obtained for Thailand, Singapore, the Philippines and VAR for Indonesia and Malaysia.
Keywords: stock price index, ASEAN, ARIMA, VAR.

Agus Suharsono, Imam Safawi Ahmad, Aryo Wibisono and Wara Pramesti
Cite this Article Agus Suharsono, Imam Safawi Ahmad, Aryo Wibisono and Wara
Pramesti, Modeling of Autoregressive Moving Average and Vector Autoregressive for
Forecasting Stock Price Index in Asean Countries, International Journal of Mechanical
Engineering and Technology, 9(11), 2018, pp. 309–319.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=11
1. INTRODUCTION
The stock market is one of the most vital components of a free-market economy. It provides
companies with access to capital in exchange for giving investors a slice of ownership. If we want
to know how the stock market is performing, we would consult an index of stocks for that whole
market or that segment of the market. Indexes are used to measure changes in the overall stock
market (IW Yu,2010)
The capital market can be an indicator for economic development a country because the
capital market provides a picture of health and economic growth of the country concerned. When
an economic condition the country is in a good position and there are government policies which
supports economic development, this can affect increasing stock prices and then increasing the
index value joint stock price of a country (Bekaert G, 2005).
In the current era of globalization, the stock market plays a very important role for investors
in investing their shares in the stock market. The better the stock price index value in a country's
stock market, the more investors will invest in the country. Also in this era of globalization,
economic interactions between countries are very important in the global economy. This causes
the transfer of capital to be faster with a large volume as well. Interaction in the economy is
characterized by the increasing openness of trade transactions and mobility of capital flows
between countries. These two factors lead to the integration of a country's capital markets with
other countries' capital markets. Capital market integration has strong implications for a country's
financial stability (Chia & Plummer 2015). Market integration in the sense that the market is truly
integrated if assets with the same ratio have the same returns (Berk I & Aydogan B, 2012).
Stock market integration continues get extraordinary attention because of its relationship with
investment international portfolio. Stock market become more integrated because the increasing
importance of capital mobility free arising from various mechanism for economic integration
including liberalization of trade barriers (Shimizu. S, 2014). Market integration is a market
situation there are no obstacles in the current finance, and risk assets to level expected return too
same, regardless of domicile.
Many things are done by a country so that the economy increase. One of them is by
establishing economic cooperation with other countries, or to innovate in the economic field to
attract foreign investors want to invest their capital. Thus the capital market will be increasingly
active, where the activity is increasing and the return obtained is increasingly promising.
Modeling the stock price index where the data is in the form of series uses more of the time series
modeling approach. If the variables analyzed are more than one type of stock, then the
multivariate time series approach is more appropriate, because it is possible to have dependencies
between one share price and another share price.
ASEAN was formed since 1967 which was initially only cooperation politics but growing
wider including economics. In ASEAN was also formed by AFTA (ASEAN Free Trade Area) or
region free trade that aims to protect economic activities in future. Finally, the establishment of
AEC (ASEAN Economic Community) who will realized at the end of 2015. For support the AEC
arranged ASEAN Integration Roadmap in the field financial which includes development capital
markets, capital account liberalization, liberalization of financial services, and exchange rate
cooperation. This collaboration will improve trade in the ASEAN region and economic
integration. Integration the economy will get stronger if capital market integration. The

Modeling of Autoregressive Moving Average and Vector Autoregressive for Forecasting Stock Price
Index in Asean Countries
integration of the stock market will be provide opportunities for companies to get capital and
share investors can invest on various securities or portfolios. In essence, AEC is ASEAN
economic integration planning to create a single market. But the problem is whether stock
markets in ASEAN already worthy of being integrated or still segmented. Therefore related
problem of decreasing world oil prices research on a decline in oil prices world and stock market
integration in ASEAN. In general, the results show that ARIMA is the best model for forecasting
the currency outflow and inflow at South Sulawesi (Suharsono. A & Suhartono, 2015)
In this study, ASEAN country stock price modeling was conducted using the ARIMA and
VAR approaches to determine the pattern of causal relationships between Indonesian, Malaysian,
Singapore, Thailand and Philippine stock price index.
2. LITERATURE REVIEW
2.1. ARIMA
ARIMA model is ARMA which differencing series data in condition of non-stationary pattern of
data with usually abbreviated as ARIMA (p,d,q). Notation p is indicates operator order of AR, q
is operator order of MA and d is operator of differencing. General formula for ARIMA is shown
in equation below (Wei, W.W.S, 2006),
tqt
d
p aBZBB )()1)(( θφ =− &
(1)
Where :
p
pp BBBB φφφφ −−−−= L2
211)(
is operator for AR(p)
)1()( 1
q
qq BBB θθθ −−−= L
is operator for MA(q)
pφ
= parameter AR order p
qθ
= parameter MA order q
ta = residual value at time t
Model identification of univariate time series using ACF (Autocorrelation Function) plot and
PACF (Partial Autocorrelation) plot. ACF is correlation between tZ dan ktZ + in same process
and different lag (Wei, W.W.S, 2006), which identified as,
)(Var)(Var
),(Cov
ktt
ktt
k
ZZ
ZZ
+
+
=ρ
Where ))())(((),(Cov ktktttktt ZZZEZEZZ +++ −−= , has value µ== + )()( ktt ZEZE at stationary
process. PACF is correlation between tZ and ktZ + after their mutual linear dependency among
121 ,,, −+++ kttt ZZZ L removed (George E. P. Box, 2016). The conditional correlation shown as,
),,,|,(Corr 121 −++++ ktttktt ZZZZZ L
or
)ˆ()ˆ(
)]ˆ(),ˆ[(
ktkttt
ktkttt
k
ZZVarZZVar
ZZZZCov
P
++
++
−−
−−
=
2.2. Vector Autoregressive (VAR)

The VAR model is actually a combination of several Autoregressive (AR) models, where these
models form a vector which between the variables affects each other. The VAR model is a
quantitative forecasting approach that is usually applied to multivariate time series data. This
model explains the interrelationship between observations on certain variables at a time with
observations on the variables themselves at previous times and also their relation to observations
on other variables at previous times (Hamilton, J.D, 1994). Vector Autoregressive (VAR) is a
statistical method used to analyze the relationship between several variables that influence each
other. The Vector Autoregressive model can be explained as follows
= + + (2)
= + + + + … + y +
In estimating the parameters of the VAR (p) model, there are two methods that can be done,
namely the Maximum Likelihood (MLE) method and the Least Squares (LS) method (Hamilton,
J.D., 1994). The Maximum Likelihood (MLE) method is used to estimate the parameters of a
model known for its density function, by maximizing the likelihood function.
3. METHODOLOGY
The data in this study used primary data taken from the Indonesia Stock Exchange and other
ASEAN Stock Exchanges, while secondary data was taken through searching in Yahoo finance
and technical investing; Data was taken from July 2012 to September 2017.
There are five responses, i.e. the Indonesia stock price index IDX(Y1,t), Malaysia stock price
index KLCI (Y2,t), Thailand stock price index SETI (Y3,t), Singapura stock price index SGX(Y4,t),
and Philipines stock price index PSE (Y5,t). The initial step taken in this study was to plot data to
see data patterns, whether stationary or not, Further analysis by looking at ACF, PACF, MACF
and MPACF to determine the order of the model the steps to be examined. The steps above are
part of testing stationarity on the mean and variant of the data. The formation of the ARIMA and
VAR models is carried out with the following analysis steps:
1. To get the first goal, which is to know the characteristics of data , the steps are as follows.
a. Time series plots.
b. Calculate descriptive statistics (average, standard deviation) every month during the
observation period.
2. Test the assumption of a constant residual variance by testing the Lagrange Multiplier,
white noise with a
3. Test Ljung Box and normally distributed using Kolmogorov Smirnov. However, when it's
residual it hasn't fulfill the assumption of white noise, then proceed to AR (p) modeling. When
residuals are not distributed normal then a dummy variable containing data is entered outlier.
4. At the ARIMA modeling stage, identification is carried out temporary model and
significant parameter checking and the assumption of white noise with the Ljung Box and test
normal distribution with Kolmogorov Smirnov, besides the residual has constant variance with
the Lagrange test Multiplier. When a residual is not normally distributed then outlier detection
RMSE is calculated in sample and out sample to determine the best model based on criteria
out sample when comparing the entire method.
4. RESULTS AND DISCUSSION
This study would apply time series theory on stock price data ASEAN countries, i.e. Indonesia,
Malaysia, Philippine, Singapore and Thailand. The data is closed price daily series starting from
June 2016 until September 2017. The data divided into two sections, first part is in sample data
will applied in order to get model. In sample data consist from July 2016 until July 2017. The

rest of last two month data is out sample as data testing for our modelling that produce before
using in sample data. Summary data in this study shown in table below :
Table 1. Descriptive Statistics Stock Price
Stock
Price
Mean Std Dev Min Max
Thailand 1614.14 115.7164 1406.18 1838.96
Malaysia 1736.943 72.5747 1614.9 1895.18
Indonesia 5706.883 444.0708 4807.23 6689.29
Singapore 3180.974 253.1911 2729.85 3615.28
Philippines 7807.147 514.3576 6563.67 9058.62
The largest mean of the ASEAN stock price index, i.e. 7807.147 for Philippine, 5706.883 for
Indonesia, 3180.974 for Singapore, 1736.943 for Malaysia and 1614.14 for Thailand. The largest
standard deviation of ASEAN stock price index, i.e. 514.3576 for Philippine, etc. This shows
that the Philippines stock price index is high with a high standard deviation. in other words, the
Philippine stock price index fluctuates greatly.
Based on Table 1. Kuala Lumpur Stock Exchange (KLSE) has smallest range between
maximum and minimum value. On another side, Philippine Stock Exchange (PSE) has biggest
interval and standard deviation. This result looks like indicate PSE is the most volatility than
another countries. Investor with high risk taker would take PSE as potential market and KLSE
as non potential market cause of minimum of volatility. Information of coefficient variation (CV)
give different volatility. Strait Time Index (STI) Singapore has CV 7.96 as the biggest value than
another countries, while KLSE still has minimum CV’s value 4.18. The small variation could
also be seen from the smallest difference between the maximum and minimum values.
From the results of data plots to find out the pattern of data obtained results,

Figure 1 Time series plot of ASEAN stock price index
It can be seen that in the time series plot there is a change in structure over a certain period of
time. Therefore, direct modeling using ARIMA or VAR can be done. Because it performs a
forecast for sample data out, the forecast results cannot capture the sample out pattern properly.
For this reason, two-stage forecasting is necessary. The first stage is using time series
regression. After that the residuals generated in the time series regression are modeled again with
ARIMA. The dummy determination in time series regression becomes important. In the picture
below is the basis for determining the dummy of time series regression variables.
40536031 52702251801 3590451
1 900
1 800
1 700
1 600
1 500
1 400
Index
Thailand
4053603152702251 8013590451
3600
3400
3200
3000
2800
2600
Index
Singapore
40536031 52702251 801 3590451
9000
8500
8000
7500
7000
6500
Index
Philippines

Figure 2 The plot of determining time series regression dummy
Based on the picture above there are 5 types of dummy variables namely t to 1-50, 51-135,
136-320, 360-finished. Besides that, other dummy additions are dummy trends and months of
occurrence of data for each observation.
In this time series modeling, the out-sample data used is 30 observations of the last stock
price. After modeling with time series regression, the ARIMA model was identified.
The following are ACF and PACF time series residual regression plots in each country,
40536031527022518013590451
6500
6000
5500
5000
Index
Indonesia
50 135 320 360
40536031527022518013590451
1900
1850
1800
1750
1700
1650
1600
Index
Malaysia
50 135 320 360
40536031527022518013590451
1900
1800
1700
1600
1500
1400
Index
Thailand
50 135 320 360
40536031527022518013590451
3600
3400
3200
3000
2800
2600
Index
Singapore
50 135 360320
40536031527022518013590451
9000
8500
8000
7500
7000
6500
Index
Philippines
50 135 320 360

Figure 3 The plot of ACF and PACF

To determine the order of VAR, an analysis with SAS was carried out and the results were as
follows,
Table 2 Order VAR
It is seen that the recommended order for VAR is 1. Next is forecasting using a combined
model of time series and VAR regression. The plot time series results between data in sample
and out sample with the results of predictions for modeling with Time Series Regression-ARIMA
and Time Series Regression- VAR are presented in the following figure,

Figure 4 The plot Time Series ARIMA and VAR
The results of the time series analysis between ARIMA and VAR are presented in the
following table along with the MAPE values for the in-sample and the out-samples data,
Table 3 MAPE In-sample and Out-sample for each country
Country
In Sample Out Sample
VAR ARIMA VAR ARIMA
Thailand 0.486 0.491 2.829 2.826
Malaysia 0.342 0.330 5.111 5.162
Indonesia 0.541 0.539 2.716 2.788
Singapore 0.546 0.542 3.486 3.410
Philippines 0.684 0.677 2.174 2.097

5. CONCLUSION
This paper has discussed the results of empirical study with two main cases, i.e. the model of
market stock ASEAN countries by using ARIMA for time series regression’s residual , and by
using VAR model. These results indicate that the ARIMA model give best prediction.
Information about the characteristics of stock market each country is important for all parties
involved when propose the model, especially in case of wave of pattern data. By knowing the
pattern, it had expected to do better calculate dummy of prediction variable(s) based on this
pattern. This paper has shown us the means to learn from data and model results, so that we know
how to make decision in policy or business for unforeseen future market stock value in. To
recapitulate, this research shows that the interpretation of time series regression by using both
model methods of residual provide future data is influenced by their stock market of each country
not by ASEAN stock market.
REFERENCES
[1] Yu IW, Fung KP, Tam CS. (2010). Assessing Financial Market Integration In Asia–Equity
markets. Journal of Banking & Finance. 34 (Februari): 2874–2885.
[2] Bekaert G, Harvey CR, Ng A. (2005). Market Integration and Contagion. Journal of Business.
78(1): 39-69
[3] Chia, S.Y., & Plummer M. (2015). Asian Economic Cooperation and Integration. Progress,
hallenges and Future Directions. Cambridge: Cambridge University Press
[4] Berk I, Aydogan B. (2012). Crude Oil Price Shocks and Stock Returns: Evidence from
Turkish Stock Market under Global Liquidity Conditions. EWI Working Paper. 15(12).
[5] Shimizu, S. (2014). ASEAN Financial and Capital Markets: Policies and Prospects of
Regional Integration. Pacific Business and Industries, 14 (54). Available at:
https://www.jri.co.jp/MediaLibrary/file/english/periodical/rim/2014/54.pdf.
[6] Suharsono. A, Suhartono, Masyita. A, (2015). Time series regression and ARIMAX for
forecasting currency flow at Bank Indonesia in Sulawesi region, AIP Conference
Proceedings, Kedah Alor, Malaysia
[7] Wei, W.W.S., (2006), Time Series Analysis: Univariate and Multivariate Methods, 2nd
ed.,
California: Addison-Wesley Publishing Company, Inc.
[8] George E. P. Box (2016), Time Series Analysis: Forecasting and Control, 5th Edition, Wiley
[9] Hamilton, J.D., (1994), Time Series Analysis, New Jersey: Princeton University Press.

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