On the Detection and Estimation of Long Memory in Stochastic Volatility (1995)
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BibTeX
@MISC{Breidt95onthe,
author = {F. Jay Breidt and Nuno Crato and Pedro De Lima},
title = {On the Detection and Estimation of Long Memory in Stochastic Volatility},
year = {1995}
}
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Abstract
Recent studies have suggested that stock markets' volatility has a type of long-range dependence that is not appropriately described by the usual Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential GARCH (EGARCH) models. In this paper, different models for describing this long-range dependence are examined and the properties of a Long-Memory Stochastic Volatility (LMSV) model, constructed by incorporating an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process in a stochastic volatility scheme, are discussed. Strongly consistent estimators for the parameters of this LMSV model are obtained by maximizing the spectral likelihood. The distribution of the estimators is analyzed by means of a Monte Carlo study. The LMSV is applied to daily stock market returns providing an improved description of the volatility behavior. In order to assess the empirical relevance of this approach, tests for long-memory volatility are described and applied to an e...
