Martingale unobserved component models

Feb 2013 | 644

Authors: Neil Shephard

I discuss models which allow the local level model, which rationalised exponentially weighted moving averages, to have a time-varying signal/noise ratio.  I call this a martingale component model.  This makes the rate of discounting of data local.  I show how to handle such models effectively using an auxiliary particle filter which deploys M Kalman filters run in parallel competing against one another.  Here one thinks of M as being 1,000 or more.  The model is applied to inflation forecasting.  The model generalises to unobserved component models where Gaussian shocks are replaced by martingale difference sequences.

JEL Codes: C01, C14, C58, D53, D81

Keywords: Auxiliary particle filter, EM algorithm, EWMA, forecasting, Kalman filter, likelihood, martingale unobserved component model, particle filter, stochastic volatility

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