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Comparing Forecasts of GARCH (1, 1)-M and GARCH (1, 1)-M-ANNs Model: A Study Based On Stock Market Data

Comparing Forecasts of GARCH (1, 1)-M and GARCH (1, 1)-M-ANNs Model: A Study Based On Stock Market Data

Samreen Fatima* and Muddasir-Uddin

Department of Statistics, University of Karachi, Pakistan

*Correspondence: Samreen Fatima, Department of Statistics, University of Karachi, Pakistan; Email: 


Portfolio managers, investors and policymakers are interested in predicting volatility to achieve higher profits or lower risk positions. Due to economic globalization and advancement in information technology, the financial market has become increasingly unstable therefore to understand the pattern of the volatility is difficult. This study aims to compare the performance of Artificial Neural Network (ANNs) and the volatility models Generalized Autoregressive Conditional Heteroscedastic in Mean (GARCH-M) to forecast the stock markets data. The data of two stock markets namely, Karachi Stock Exchange 100 (KSE-100) of Pakistan and Standard and Poor’s 500 (S and P 500) of USA stock market covering the period 1st January 2013 to 31st, December 2019 are considered for analysis. Various forms of GARCH-M models are applied by inserting conditional standard deviation, conditional variance, or conditional log variance in the conditional mean equation. Moreover, enhancement in the forecasting performance by combining the GARCH-M and ANNs (hybrid model), developed GARCH-M-ANNs model could be seen clearly. As per Akaike Information Criterion (AIC) and Schwarz Bayesian Information Criterion (SBIC), the study shows that GARCH (1, 1)-M estimations by changing conditional mean equations are found to be the most appropriate model. The three measures criterion namely: root mean squares error (RMSE), mean absolute error (MAE) and relative mean absolute error (RMAE) are used for model robustness measurement. The estimation results show that both in-sample and out-sample RMSE, MAE and RMAE are minimum in GARCH (1, 1)-M-ANNs models. Furthermore, empirical analysis reveals that the forecast result of GARCH (1, 1)-M-ANNs models of all three forms give a similar result. The results obtained here are useful for the market practitioners, policymakers and investors. 

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Pakistan Journal of Zoology


Vol. 54, Iss. 6, Pages 2501-3000


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