A test for improved multi‐step forecasting

John Haywood and Granville Tunnicliffe Wilson

Journal of Time Series Analysis, 2009, vol. 30, issue 6, 682-707

Abstract: Abstract. We propose a general test of whether a time‐series model, with parameters estimated by minimizing the single‐step forecast error sum of squares, is robust with respect to multi‐step prediction, for some specified lead time. The test may be applied to a, possibly seasonal, autoregressive integrated moving average (ARIMA) model using the parameters and residuals following maximum likelihood estimation. It is based on a score statistic, evaluated at these estimated parameters, which measures the sensitivity of the multi‐step forecast error variance with respect to the parameters. We derive the large sample properties of the test and show by a simulation study that it has acceptable small sample size properties for higher lead times when applied to the integrated moving average or IMA model that gives rise to the exponentially weighted moving average predictor. We investigate the power of the test when the IMA(1,1) model has been fitted to an ARMA(1,1) process. Further, we demonstrate the high power of the test when an AR is fitted to a process generated as the sum of a stochastic trend and cycle plus noise. We use frequency domain methods for the derivation and sampling properties of the test, and to give insight into its application. The test is illustrated on two real series, and an R function for its general application is available from http://msor.victoria.ac.nz/Main/JohnHaywood.

Date: 2009
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https://doi.org/10.1111/j.1467-9892.2009.00634.x

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