Modeling and Volatility Analysis of Oil Companies in Pakistan

by Firdos Khan1, Zahid Asghar .

Abstract: We focus on modeling of conditional mean and conditional variance of the share prices of two stocks, i.e. Shell Gas (LPG) Pakistan and Attock Petroleum (AP) from Karachi Stock Exchange by using ARIMA and ARCH models. We have daily data for shell gas (LPG) Pakistan and Attock Petroleum (AP) from 3rd of August 1998 to 31st of January 2007. Firstly we have constructed ARIMA modeling. Unit root testing with different lag length criteria has been performed. We find that there are more than one potential models which fit to this data. The performances of these models are not different from each other. The best model for AP series is ARIMA(1,1,0) and for LPG ARIMA((1,2),1,0) is the best model among the competing models. Secondly we have measured the volatility of the stocks by ARCH family of models. Maximum likelihood method of estimation is used to estimate the unknown parameters of the models. Different lag length criteria like AIC, BIC etc are used to find the best possible model. The potential models are then analyzed on the basis of their forecast performance. GARCH model is the best model for AP series and EGARCH model is the best model for LPG series among the competing models. This study is an important application of all the modern time series econometric tools. Moreover effort is made to remove a misnomer (which our old econometricians and books show that true model is known) that there is only one model which fits the data.

Key Words: ARIMA Models, ARCH Models, Unit Root test, AIC, BIC, ARCH-LM test, Volatility, MSE, RMSE, MAE, TIC, TGARCH Model, LM-Test, GARCH model, EGARCH model, JGR-GARCH model, P-Value, White noise, Stationarity

Firdos Khan,
Zahid Asghar,

Editor: Meintanis,Simos G,

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