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Home  >  Volume 43

23. Applications of Long-Memory Stochastic Volatility Models BY Onyeka-Ubaka J. N. and Okafor R. O. JNAMP Vol. 43,(Sept. and Nov., 2017), pp155 – 168
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Recent empirical studies seem to suggest that the squares of high-frequency financial data are long-range dependent such that the conventional generalized autoregressive conditional heteroskedasticity (GARCH) and exponential GARCH (EGARCH) models collapsed in capturing the stylized facts (fat tails, volatility clustering, leverage effects, long memory and co-movements in volatility). In this paper, fractionally integrated models are considered on assumption that the volatility process is assumed not only to be stochastic, but also to have long-memory features and properties. The study establishes strong consistent estimators for the parameters of the long-memory stochastic volatility models using maximum likelihood estimation method. The scaled truncated log-ARFIMA(k,d,l) models forecast implied volatility for both short and long horizons better that other volatility forecast models as evinced from the mean absolute forecast error (MAFE) and mean square forecast error (MSFE). We also established that the moving average method is not inferior to the more sophisticated methods such as GARCH and log-ARFIMA models for the forecast of long horizons. 

Keywords: Long-range dependence, volatilities, stochastic, GARCH