Comparisons of Hyvärinen and pairwise estimators in two simple linear time series models

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The aim of this paper is to compare numerically the performance of two estimators based on Hyvärinen's local homogeneous scoring rule with that of the full and the pairwise maximum likelihood estimators. In particular, two different model settings, for which both full and pairwise maximum likelihood estimators can be obtained, have been considered: the first order autoregressive model (AR(1)) and the moving average model (MA(1)). Simulation studies highlight very different behaviours for the Hyvärinen scoring rule estimators relative to the pairwise likelihood estimators in these two settings.