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Unformatted text preview: The Lahore Journal of Economics 12 : 2 (Winter 2007) pp. 115-149 Estimating and Forecasting Volatility of Financial Time Series in Pakistan with GARCH-type Models G.R. Pasha * , Tahira Qasim ** and Muhammad Aslam *** Abstract In this paper we compare the performance of different GARCH models such as GARCH, EGARCH, GJR and APARCH models, to characterize and forecast financial time series volatility in Pakistan. The comparison is carried out by comparing symmetric and asymmetric GARCH models with normal and fat-tailed distributions for the innovations, over short and long forecast horizons. The forecasts are evaluated according to a set of statistical loss functions. Daily data on the Karachi Stock Exchange (KSE) 100 index are analyzed. The empirical results demonstrate that the use of asymmetry in the GARCH models and the assumption of fat-tail distributions for the innovations improve the volatility forecasts. Overall, EGARCH fits the best while the GJR model, with both normal and non-normal innovations, seems to provide superior forecasting ability over short and long horizons. Keywords: APARCH; EGARCH; Fat-tailed distribution; Forecast; Forecast horizon; GARCH; GJR; KSE 100; Volatility. Introduction Financial markets play a crucial role in any countrys economy. Monetary policies are generally based on stock exchange indices, foreign exchange rates, price indices, inflation rates, interest rates, etc. Further it is generally assumed that the ultimate goal for monetary policy is price stability. Empirical studies have concluded that a large change in prices today tends to be followed by a larger change in the * Dean of Sciences and Agricultures/Chairman, Department of Statistics, Bahauddin Zakariya University, Multan. ** HEC Ph.D. Scholar, Department of Statistics, Bahauddin Zakariya University, Multan. *** Assistant Professor, Department of Statistics, Bahauddin Zakariya University, Multan. G.R. Pasha, Tahira Qasim and Muhammad Aslam 116 financial sector for which a time series study needs to be conducted. One has to carry a time series study of all such financial changes. Some well- known characteristics are common to many financial time series. Even a cursory look at data suggests that some time periods are riskier than others resulting in a variation in the expected values of the error terms. Moreover, these risky times are not scattered randomly across quarterly or annual data. Instead, there is a degree of autocorrelation in the riskiness of financial returns. Volatility clustering is often observed. Financial time series often exhibit leptokurtosis, meaning that the distribution of their returns is fat-tailed. Moreover, the so-called leverage effect refers to the fact that changes in stock prices tend to be negatively correlated with changes in volatility. The econometric challenge is to specify how the information is used to estimate and forecast the mean and variance of the return, conditional on the past information. Currently the most powerful known techniques used to information....
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