State space models for time series with patches of unusual observations

Jeremy Penzer

Journal of Time Series Analysis, 2007, vol. 28, issue 5, 629-645

Abstract: Abstract. An alternative to leave‐k‐out diagnostics for detecting patches of outlying points in time series is developed. We propose that unusual behaviour should be modelled by the addition of shocks. By including shocks in the transition equation of a state space model, we admit the possibility of a persistent change associated with a patch of outliers. Persistent change may take the form of a level shift or a change in seasonal pattern. We provide an efficient mechanism for computing diagnostic statistics associated with the addition of k shocks using a simple adaptation of the Kalman filter. Statistics for detecting unspecified patterns of shocks and an interpretation of the output of the associated smoothing algorithm are derived. Illustrations using real series are given.

Date: 2007
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