Modeling Volatility and Forecasting of Stock Price_A Case Study on Two Private Commercial Banks in...

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


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


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


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



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



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


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


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


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

Modeling Volatility and Forecasting of Stock Price_A Case Study on Two Private Commercial Banks in...

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