Time Series Models with a Common Stochastic Variance for Analysing Economic Time Series

Siem Jan Koopman and Charles Bos

No 02-113/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This discussion paper led to an article in Statistica Neerlandica (2003). Vol. 57, issue 4, pages 439-469.

The linear Gaussian state space model for which the common variance istreated as a stochastic time-varying variable is considered for themodelling of economic time series. The focus of this paper is on thesimultaneous estimation of parameters related to the stochasticprocesses of the mean part and the variance part of the model. Theestimation method is based on maximum likelihood and it requires thesubsequent uses of the Kalman filter to treat the mean part andsampling techniques to treat the variance part. This approach leads tothe evaluation of the exact likelihood function of the model subject tosimulation error. The standard asymptotic properties of maximumlikelihood estimators apply as a result. A Monte Carlo study is carriedout to investigate the small-sample properties of the estimationprocedure. We present two illustrations which are concerned with themodelling and forecasting of two U.S. macroeconomic time series:inflation and industrial production.

Keywords: Autoregressive integrated moving average; Importance sampling; Industrial production; Inflation; Kalman filer; Monte Carlo simulation; Simulation smoothing; State space; Stochastic volatility; Unobserved components time series. (search for similar items in EconPapers)
JEL-codes: C15 C32 C51 E23 E31 (search for similar items in EconPapers)
Date: 2002-11-12
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