Long memory estimation of stochastic volatility for index prices

Abstract

One of the typical ways of measuring risk associated with persistence in financial data set can be done through studies of long memory and volatility. Finance is a branch of economics concerned with resource allocation which deals with money, time and risk and their interrelation. The investors invest at risk over a period of time for the opportunity to gain profit. Since the last decade, the complex issues of long memory and short memory confounded with occasional structural break had received extensive attention. Structural breaks in time series can generate a strong persistence and showing a slower rate of decay in the autocorrelation function which is an observed behaviour of a long memory process. Besides that, the persistence in volatility cannot be captured easily because some of the mathematical models are not able to detect these properties. To overcome these drawbacks, this study developed 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 the persistence property of the data. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using least square estimator (LSE) and quadratic generalized variations (QGV) method respectively. Whereas, the long memory parameter namely Hurst parameter is estimated by using several heuristic methods and a semi-parametric method. The procedure of constructing LMSV model and the estimation methods are applied to the real daily index prices of FTSE Bursa Malaysia KLCI over a period of 20 years. The findings showed that the volatility of the index prices exhibit long memory process but the returns of the index prices do not show strong persistence properties. The root mean square errors (RMSE) obtained from various methods indicates that the performances of the model and estimators in describing returns of the index prices are good.