The Simulation Smoother for Time Series Models

Abstract

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Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models

“…de Jong and Shephard (1995) and Durbin and Koopman (2002) have developed simulation smoothing methods for sampling α from g(α|y * ; ψ) in a computationally efficient way. The Kalman filter calculates g(y * ; ψ) via its evaluation of the likelihood function for the linear state space model (A.4).…”

Estimation of stochastic volatility models via Monte Carlo maximum likelihood

“…Generate a sample G "( G , 2 , G 2 ) from the importance density p % ( " y, ) referring to the approximating model of step 1. A specific version of the simulation smoother of de Jong and Shephard (1995) is used to generate this sample; see Appendix A for details. 4.…”

Dating Business Cycles in Historical Perspective: Evidence for Switzerland

“…In the second step a preliminary set of turning points is identified by means of the business cycle dating algorithm of Artis et al (2004). At this stage we also apply the simulation smoother of de Jong and Shephard (1995) in order to assess uncertainty around turning points arising from prefiltering. In the third step we select the most likely candidates for final identification of turning points using the original time series.…”

“…Recall that the dating algorithm is applied to a prefiltered time series, or a trend component µ t in Equation (2), where cycles with a periodicity of, say, 5 quarters have been dampened. Prefiltering introduces uncertainty in the identification of the turning points that can be assessed by means of the simulation smoother suggested in de Jong and Shephard (1995). The simulation smoother is a Monte Carlo procedure that repeatedly draws simulated samples from the posterior distribution of the trend componentμ (i) t ∼ µ t |y 1 , ..., y T .…”