Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series B, Pt. 1, 1--10

BAYESIAN ANALYSIS OF LONG MEMORY STOCHASTIC VOLATILITY MODELS

By

MIKE K.P. SO, The Hong Kong University of Science & Technology, Hong Kong

SUMMARY. Recent studies demonstrate that volatility exhibits long-range dependence. This article investigates a long memory stochastic volatility model in which the stochastic process governing the volatility is an Autoregressive Fractionally Integrated Moving Average process. Bayesian estimation via Monte Carlo Markov Chain sampling methods is proposed. Besides, Bayesian prediction and smoothing are introduced in the article. The methodologies are applied to daily returns data for illustration.

AMS (1991) subject classification. Primary 62M10; secondary 62F15, 90A20.

Key words and phrases. Bayesian estimation, fractional differencing, Gibbs sampling, Monte Carlo Markov chain, prediction, smoothing.

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