Comparative study of exponential smoothing models and Box Jenkins ARIMA model of partitioned data of daily stock prices of the CRDB Bank in Tanzania ∗
DOI:
https://doi.org/10.48165/Keywords:
Time series analysis, ARIMA model, Simple, Double and Damped trend linear exponential smoothing methods, ACF and PACFAbstract
Data mining techniques and other analytical techniques have played a sig nificant role in analysing data from different sources. Data from stock market consist of high volatility and hence it needs a special care to fit a model for forecasting future stock prices values. In the stock market, investors trade to get positive returns through buying at a lower price and selling at a higher price. However, not all investors get positive re turns on their investment in stock market because of large amount of risk involved in the stock market due to vast fluctuation in the stock market prices.This study is conducted to compare and select the best model among autoregressive integrated moving average (ARIMA), single exponential smoothed model (SES), double exponential smoothed model (DES), and Damped trend linear exponential smoothed model. The modelling process was preceded by analysing the time series which revealed the presence of non-stationarity. The resultant models were found as ARIMA(1,1,2), Simple Exponential Smoothing (SES) and Double exponential smoothing (DES) whose parameters’ estimates were also found to be statistically significant. Akaike’s Information Criterion (AIC) and Bayesian Infor mation Criterion (BIC) were used to select the best model among all the three fitted models. The performance of the fitted model is analyzed and the market behavior for future forecast is studied. ARIMA(1,1,2) is selected as the best model for daily stock forecasting for the CRDB bank in Tanzania.
References
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[stockpriceF,stockpriceMSE] = forecast(ARIMA stockprice,20,‘Y0’,stockprice); UB = stockpriceF + 1.96*sqrt(stockpriceMSE);
LB = stockpriceF - 1.96*sqrt(stockpriceMSE);
dateF = date(end) + days(1:2o);
figure
h4 = plot(date,stockprice,‘Color’,[.75,.75,.75]);
hold on
h5 = plot(dateF,stockpriceF,‘r’,‘LineWidth’,2);
h6 = plot(dateF,UB,‘k–’,‘LineWidth’,1.5);
plot(dateF,LB,‘–’,‘LineWidth’,1.5);
legend([h4,h5,h6],‘stock price for CRDB’,‘Forecast’,...
‘Forecast Interval’,‘Location’,‘Northwest’)
title(‘Stock price for CRDB Forecast’)
xlabel(‘years’)
ylabel(‘stock price’)
hold off
Appendix 2: Code for R Software
code for software
#loading data into R software
library(readxl)
p3 <- read excel(“C:/Users/hp/Desktop/gebo/juma/p3.xlsx”)
view(p3)
#for performing ARIMA and AUTOARIMA
attach(p3)
library(readxl)
library(forecast)
# Defining variables
Y <-closing price
d.Y<- diff(Y)
dd.Y<-diff(d.Y)
t <-date
arimafit<- auto.arima(Y)
fcast<- forecast(arimafit)
plot(fcast)
standardize residuals<-residuals(arimafit)
hist(standardize residuals,plot = TRUE,main = “Histogram of standardize residual”) y=rnorm(1885)
qqplot(standardize residuals,y,plot = TRUE)
acf(residuals(arimafit),plot = TRUE,lag.max = 20)
Box.test(residuals(arimafit),lag = 20,type = “Ljung-Box”,fitdf =1)
tsdiag(arimafit)
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