Modeling Volatility and Forecasting of Stock Price: A Case Study on Two Private Commercial Banks in Bangladesh
Md. KamruzzamanLecturer
Department of Statistics, Jagannath University
Saifur Rahman ShohelGraduate Student
School of Business, Uttara University
Md. Mohsan KhudriAssistant Professor
School of Business, Uttara University
Thanks to the Organizers of this conference
PHASE 1: INTRODUCTION
PHASE 2: DATA & VARIABLES
PHASE 3: METHODOLOGY
PHASE 4: ANALYSIS & DISCUSSION
PHASE 5: CONCLUSION
PRESENTATION OUTLINE
OVERVIEW
Forecasting on stock price is a common practice around the world.
We have considered Autoregressive Integrated Moving Average (ARIMA) model
to forecast month ended stock price.
Banks play major rules in economy
of BangladeshTotal 66 banks in
Bangladesh.
More than 6000 branches
Introduction
Introduction
To find out the appropriate forecasting model for the month ended stock market
price of the selected banks.
To forecast the month ended stock price for next 24 months (Jan-2014 to Dec-2015).
To see the forecasting performance of the selected models.
OBJECTIVES OF THE STUDY
Introduction
LITERATURE REVIEW
In “Time series forecasting using a hybrid ARIMA and neural network model”
(2003), Zhang said that Autoregressive integrated moving average (ARIMA) is one
of the popular linear models in time series forecasting during the past three
decades.
According to Pai & Lin in “A hybrid ARIMA and support vector machines model in
stock price forecasting”(2005), The real data sets of stock prices were used to
examine the forecasting accuracy of the proposed model. The results of
computational tests are very promising.
According to Al-Zeaud in “Modeling volatility using ARIMA model in European
journal of Economics” (2011); The study presents the Box-Jenkins model as one of
the forecasting techniques, which we can use, in the financial time series.
AND SO ON………………………..
Data & Variables
VARIABLES TIME PERIOD
Month ended Stock price of National Credit & Commerce Bank Ltd. (NCC) JAN-2001 to DEC-2013
Month ended Stock price of Mutual Trust Bank Ltd. (MTB) JUL-2003 to DEC-2013
DATA SOURCE:Dhaka Stock Exchange (DSE) library of Bangladesh.
DATA & VARIABLES
Bank selection procedure:
Simple random sampling
Out of 66 banks, 2 banks are selected
Package: Statistical package for social science (SPSS)
Methodology
ARIMA Methodology:Time Series Data
Checking stationarity Augmented Dickey-Fuller Test (ADF Test)
Obtaining stationarity Differencing method
FORECASTING METHODOLOGY
ARIMA Model is given below:
qtqtttptd
ptd
td
td eeeec ....... 22112211
Methodology
FORMULATION OF ARIMA MODEL
Order of the autoregressive
part
Degree of difference involved
Order of the moving average
AR MAI
d qp
ARIMA (p,d,q)
Methodology
.
The AIC is given by:
Where , L = maximum likelihoodm = is the number of terms estimated in the model.
SELECTION OF BEST ARIMA MODEL
The model having the minimum AIC value will be treated as the best model.
Packages used: Statistical package for social science (SPSS) R
2m2logLAIC
Akaike’s Information Criterion (AIC)
Measure of forecast error
Analysis & Discussion
CHECKING STATIONARITY OF DATA
Figure: Time series plot of month ended stock price of National Credit & Commerce Bank Ltd.
Figure: Time series plot of month ended stock price of Mutual Trust Bank Ltd.
Figure: Time series plot of observed data
Analysis & Discussion
Null-hypothesis = Data is Non-Stationary,Alternative Hypothesis = Data is Stationary,Significance level, = 0.05α
Results of Augmented Dickey-Fuller (ADF) Test:
CHECKING STATIONARITY OF DATA
Since the p>α for NCC Bank, so we can’t reject Null-hypothesis. So data is non-stationary.
Since the p>α for Mutual Trust Bank, so we can’t reject Null-hypothesis. So data is non-stationary.
Variable p-value Note Data type
NCC 0.5981 p>α NON-STATIONARY
MTB 0.4488 p>α NON-STATIONARY
Analysis & Discussion
OBTAINING STATIONARITY USING DIFFERENCING METHOD
We can difference the data to obtain stationarity. That is, given the series , we create the new series , using the equation below:
1 ttt YYZ
tY tZ
Analysis & Discussion
Figure: Time series plot of first difference month ended stock price of National Credit & Commerce Bank Ltd.
Figure: Time series plot of first difference month ended stock price of Mutual Trust Bank Ltd.
Figure: Time series plot of first differenced data
OBTAINING STATIONARITY USING DIFFERENCING METHOD
Analysis & Discussion
Null-hypothesis = Data is Non-Stationary,Alternative Hypothesis = Data is Stationary,Significance level, = 0.05α
Results of Augmented Dickey-Fuller Test after obtaining stationarity:
Since p<α for NCC Bank, so we can reject Null-hypothesis. So data is now stationary.
Since p<α for Mutual Trust Bank, so we can reject Null-hypothesis. So data is now stationary.
Variable p-value Note Data type
NCC 0.01 p<α STATIONARY
MTB 0.01 p<α STATIONARY
OBTAINING STATIONARITY USING DIFFERENCING METHOD
Analysis & Discussion
AIC VALUE FOR NCC BANK
q=0 q=1 q=2 q=3
p=0 1723.91 1722.084 1723.614 1724.488
p=1 1722.643 1723.863 1721.831 1723.596
p=2 1723.085 1721.68 1724.9 1725.596
p=3 1723.753 1723.629 - -
AIC VALUE FOR MTB
q=0 q=1 q=2 q=3
p=0 1369.889 1370.09 1371.429 1373.166
p=1 1369.899 1371.835 1372.507 -
p=2 1371.732 1372.559 1368.411 -
p=3 1372.655 1373.81 - -
DETERMINATION OF APPROPRIATE ARIMA MODEL
2,1,2ARIMA
1,1,2ARIMA
Analysis & Discussion
ESTIMATION AND DIAGNOSTIC CHECKING
Parameter Estimated value Standard error p value
NCC BankARIMA (2,1,1)
AR1 -1.0161 0.1119 0.000
AR2 -0.2087 0.0795 0.002
MA1 0.8887 0.0873 0.000
Parameter Estimated value Standard error p value
MTBARIMA (2,1,2)
AR1 0.2462 0.1030 0.004
AR2 -0.7774 0.0891 0.000
MA1 -0.1790 0.0606 0.000
MA2 0.9329 0.0585 0.000
Analysis & Discussion
FORECASTED MONTH ENDED STOCK PRICE NCC BANK
Model: ARIMA (2,1,1)
Point Forecast95% Confidence Interval
Lower Limit Higher LimitJan 2014 14.00509 -105.2613 133.2715
Feb 2014 13.23148 -145.0571 171.5201Mar 2014 13.82870 -170.5866 198.2440
Apr 2014 13.38329 -200.0236 226.7902May 2014 13.71125 -220.4542 247.8767Jun 2014 13.47094 -243.1200 270.0619
Jul 2014 13.64669 -261.2183 288.5116Aug 2014 13.51826 -280.0930 307.1295Sep 2014 13.61209 -296.4969 323.7211
Oct 2014 13.54355 -313.0065 340.0936Nov 2014 13.59361 -328.0646 355.2518Dec 2014 13.55704 -342.9493 370.0634
Jan 2015 13.58375 -356.9090 384.0765Feb 2015 13.56424 -370.5941 397.7226
Mar 2015 13.57849 -383.6426 410.7996Apr 2015 13.56808 -396.3939 423.5301May 2015 13.57569 -408.6761 435.8275
Jun 2015 13.57013 -420.6713 447.8115Jul 2015 13.57419 -432.3008 459.4491
Aug 2015 13.57123 -443.6654 470.8079Sep 2015 13.57339 -454.7322 481.8790
Oct 2015 13.57181 -465.5594 492.7030Nov 2015 13.57297 -476.1358 503.2817Dec 2015 13.57212 -486.4967 513.6410
Comparison between observed and forecasted stock price of NCC Bank
Analysis & Discussion
FORECASTED MONTH ENDED STOCK PRICE OF MUTUAL TRUST BANKModel: ARIMA (2,1,2)
Point
Forecast95% Confidence Interval
Lower Limit Higher Limit
Jan 2014 23.87675 -84.31243 132.0659Feb 2014 30.75322 -127.47401 188.9805Mar 2014 26.55562 -180.83267 233.9439Apr 2014 20.17617 -226.19299 266.5453May 2014 21.86904 -251.41566 295.1537Jun 2014 27.24545 -269.43351 323.9244Jul 2014 27.25294 -295.16616 349.6720
Aug 2014 23.07493 -324.96286 371.1127Sep 2014 22.04055 -347.38565 391.4667Oct 2014 25.03406 -362.88970 412.9578Nov 2014 26.57519 -380.25646 433.4068Dec 2014 24.62731 -401.83960 451.0942Jan 2015 22.94963 -421.72467 467.6239Feb 2015 24.05098 -436.87417 484.9761Mar 2015 25.62641 -451.09635 502.3492Apr 2015 25.15803 -467.78252 518.0986May 2015 23.81791 -484.97265 532.6085Jun 2015 23.85213 -499.66108 547.3654Jul 2015 24.90242 -512.67048 562.4753
Aug 2015 25.13438 -526.54981 576.8186Sep 2015 24.37495 -541.36345 590.1133Oct 2015 24.00765 -555.20746 603.2228Nov 2015 24.50764 -567.60412 616.6194Dec 2015 24.91629 -579.92545 629.7580
Comparison between observed and forecasted stock price for MTB
Conclusion
CONCLUSION
After fitting various ARIMA models , the following models have been found as the best models for NCC and MTBL, respectively as per AIC values :
Performances of the selected forecasting models have been checked by comparing observed data with predicted data of the selected banks.
We have found that the forecasted data is well fitted with the observed data.
2,1,2ARIMA
1,1,2ARIMANCC Bank
Mutual Trust Bank
Q/A
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