Modeling and estimation on long memory stochastic volatility for index prices of FTSE Bursa Malaysia KLCI

Abstract

Long memory and volatility have been used to measure risks associated with persistence in financial data sets. However, the persistence in volatility cannot be easily captured because some mathematical models are not able to detect these properties. To overcome this shortfall, this study develops a procedure to construct long-memory stochastic volatility (LMSV) model by using fractional Ornstein-Uhlenbeck (fOU) process in financial time series to evaluate the degree of persistence property of the data. Procedures for constructing the LMSV model and the estimation methods were applied to the real daily index prices of FTSE Bursa Malaysia KLCI over a period of 20 years. The least square estimator (LSE) and quadratic generalised variations (QGV) methods were used to estimate the drift and diffusion coefficient of the volatility process respectively. The long memory parameter was estimated by the detrended fluctuation analysis (DFA) method. The findings show that the volatility of the index prices exhibited a long memory process but the returns of the index prices did not show strong persistence properties. The root mean square errors (RMSE) obtained from various methods indicated that the performances of the model and estimators in describing returns of the index prices were good.