Far East Journal of Theoretical Statistics
Volume 3, Issue 1, Pages 187 - 212
(July 1999)
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A METHOD TO ESTIMATE RANDOM WALK STOCHASTIC VOLATITLITY MODELS
Manabu Asai (Japan)
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Abstract: Some empirical evidences indicated the high persistence in
asset return volatility. Engle and Bollerslev [15] proposed to use the
integrated GRACH (IGARCH) models from conditional volatility. Geweke [16] and
Pantula [29] suggested the integrated log GARCH (ILAGARCH) models, which are the
logarithmic extension of the IGARCH models. Harvey, Ruiz and Shephard [18] and
Ruiz [33] modelled as the logarithm of unobserved volatility follows a random
walk process, which is called the random walk stochastic volatility (RWSSV)
mode. As wit other SBV modes, the likelihood function of the RWSV model is
difficult to evaluate, In this paper, we briefly review the estimation methods
for RWSV modes, We derive an ILGARCH representation of a class of RWSV models,
including linear regression models with ARMA(p, q)-RWSV errors. We propose a new
QML method via the ILGARCH approach. Our Monte Carlo results indicate the QML
estimator via the ILGARCH approach performs well. In view of the relative
efficiency , for the parameter values found in empirical analysis, our
estimators are superior to those of the method of Moments estimator and those of
the QML estimator based on the Kalman filter. We develop procedures for testing
the integration of log-volatility. We present an empirical example of daily
Deutsche mark /U.S. dollar exchange rates. |
Keywords and phrases: log-GARCH models, quasi-maximum likelihood, random walk,,
stochastic volatility |
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