Fractional integration and long memory models of stock price volatility : the evidence of the emerging markets

Following the important work on unit roots and cointegration which started in the mid-1980s, a great deal of econometric works has been devoted to the study of the subtleties and varieties of near nonstationarity and persistence that characterize so many economic and financial time series. In recent years research activity has gained importance with outstanding contributions made on estimation and testing of a wide variety of long memory processes, together with many interesting and imaginative applications over a wide variety of different fields of economics and finance. For these reasons, this study provides empirical evidence to an aspect of fractional differencing and long memory processes, or the long memory of volatility. Evidence of long memory persistence is explored using stock price indices for eight emerging economies in both Asian and Latin American markets. The concern with the presence of long memory in higher moments of return series was first drawn by Ding, Granger and Engle (1993), using asset returns. Baillie, Bollerslev and Mikkelsen (1996) developed the fractionally integrated GARCH, or FIGARCH, process to represent long memory in volatility. The measure of long-memory persistence in the volatility is employed either using the original rescaled range statistic by Hurst (1951) and its modified version proposed by Lo (1991). Further analysis of the presence of long memory persistence is conducted using autocorrelation analysis. All the findings point in the same direction, that is, the existence of long memory in volatility irrespective of the measure chosen. Estimation of different models of volatility is undertaken beginning with the ARCH specification and until the FIGARCH model. The results show the effects to be higher in Latin American countries than in the Asian ones. This result seems consistent with the degree of intervention in the Latin American markets, known to be much higher.Other possible explanations for the occurrence of long term persistence are also pursued such as the Regime Switching modelisation proposed first by Hamilton and Susnel (1994) with the SWARCH approach. Results show that this approach can bring another possible explanation for persistence, specially in economies like Brazil that, have very different regimes for the period covered in this study