New Zealand Statistical Association
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John Haywood
Statistics, Victoria University of Wellington

A Test for Improved Time Series Forecasting at Higher Lead Times

Joint work with Granville Tunnicliffe Wilson, Lancaster University, UK.

Tiao & Xu (1993, Biometrika) proposed a test of whether a time series model, estimated by maximum likelihood, was robust with respect to multi-step prediction. Their test statistic was based on the change in parameter estimates when the model parameters were chosen to minimise the L-step forecast error sum of squares, for some lead-time L greater than one, rather than the 1-step forecast error sum of squares. Positive size distortions were reported for their statistic at lead time two, and they suggested that more work was required before their test could be used at lead times greater than two.

We consider a score version of this test, based on an approximation to the reduction in the L-step forecast error sum of squares, rather than the change in parameters. The test can be applied following maximum likelihood parameter estimation without re-estimating the model for L-step prediction. We show that the test has accurate size, or is conservative, when applied to higher lead times, and present cases where it has much greater power for detecting model inadequacy than the standard portmanteau test. The statistic is derived by frequency domain methods that provide insight into its distributional properties.

Keywords: Diagnostic statistic; EWMA; Frequency domain; Model robustness; Multi-step errors.