Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 1, 127-144

MONTE CARLO POSTERIOR INTEGRATION IN GARCH MODELS

By

PETER MULLER, Duke University, Durham
and
ANDY POLE, Invictus Partners, New York

SUMMARY. Recent developments in estimating non-linear, non-normal dynamic models have used Gibbs sampling schemes over the space of all parameters involved in the model (Carlin, Polson and Stoffer, 1992) as well as Monte Carlo integration based on propagating a Monte Carlo sample on the parameter vector qt through the stages of the dynamic model. Both approaches have advantages. The first because it enables a convenient Gibbs sampler implementation. The latter because it splits the problem into a series of simulation problems, one for each time step, thus having computational effort only increase linearly with the length of the time series. Aslo, propagating a monte Carlo sample through the dynamic model allows for unrestricted generality in the distributional form of evolution noise and likelihood. In this paper we develop schemes along both lines to apply to the analysis of GARCH (generalized autoregressive conditional heteroskedasticity) models for daily exchange rate data.

AMS (1991) subject classification. 60G35, 62f15, 62P05, 90A20.

Key words and phrases. Exchange rate data; General dynamic model; Markov Chain Monte Carlo; Metropolis; State space model.

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