Non-linearities and GARCH effects in the emerging stock markets of South Asia

Abstract

Up to the beginning of the last decade, financial economics was dominated by linear paradigm, which assumed that economic time series conformed to linear models or could be well-approximated by a linear model. However, there is increasing evidence that asset returns may be better characterized by a model which allows for non-linear behaviour. Though more efforts are now being directed towards the Asian stock markets in the light of their increasing importance to the investment world and the world economy, there is an extremely sparse literature, which utilizes recent advances in non-linear dynamics to examine the data generating process of the South-Asian stock markets. This study investigates the presence of non-linear dependence in three major markets of South Asia: India, Sri Lanka, and Pakistan. It was, however, realized that merely identifying non-linear dependence was not enough. Previous research has shown that the presence of non-linear characteristics usually takes the form of ARCH/GARCH (Autoregressive Conditional Heteroscedasticity or Generalized Autoregressive Conditional Heteroscedasticity) type conditional heteroscedasticity. Keeping this in view, this study investigates whether the non-linear dependence is caused by predictable conditional volatility. It has been found that the simple GARCH (1, 1) model has fitted all the market return series adequately and accounted for the non-linearity found in the series. The findings reveal the following: ‣ The application of the BDS test developed by Brock, et al., (1996) strongly rejects the null hypothesis of independent and identical distribution of the return series as well as the linearly filtered return series for all the markets under study. ‣ With the possibility of linear dependence causing the rejection of independent and identical distribution (IID) being eliminated by linear filtering, the study also shows that non-stationarity of return series is also not a cause for non-IID behaviour by applying Augmented Dickey Fuller test and Phillips-Perron test. This implies the presence of non-linear dependence in the return series. For researchers in the developing countries, it is time to embrace the shift to non-linearity as it would provide a better understanding of the underlying dynamics of financial time series. However, the results are not necessarily inconsistent with efficient market hypothesis, simply because non-linearity does not essentially imply predictability as the future price changes can be predictable but only with a time horizon too short to allow for excess profits. The implications of non-linear dependence and presence of GARCH effects go beyond the issue of market efficiency. The common assumption of constant variance underlying the theory and practice of option pricing, portfolio optimization, and value-at-risk (VaR) calculations needs to be revised. If the assumed stochastic processes do not adequately depict the full complexity of the true generating processes, then any derivatives in question may be mis-priced.