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Biometrika 1999 86(2):474-482; doi:10.1093/biomet/86.2.474
© 1999 by Biometrika Trust
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Miscellanea. Time series with additive noise

MKP So

Department of Information and Systems Management, The Hong Kong University of Science & Technology, Clear Water Bay, Hong Kong, ROC E-mail: immkpso@ust.hk

We put forward a state space model where the unobservable state variable can be any Gaussian stochastic process. We discuss both maximum likelihood estimation and Bayesian inference for this generalised model. The methodology developed in this paper is particularly important for the class of long memory plus noise models. Armed with the simulation smoother introduced in this paper, we can estimate a class of non-Gaussian measurement time series models with long memory in the state equation.

Key Words: Autoregressive fractionally integrated moving average; Kalman filter; Long memory; Long-range dependence; Markov chain Monte Carlo; Outlier detection; State space model; Stochastic volatility model.


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