The Hyvärinen scoring rule in Gaussian linear time series models

In this work we study stationary linear time-series models, and construct and analyse “score-matching” estimators based on the Hyvärinen scoring rule. We consider two scenarios: a single series of increasing length, and an increasing number of independent series of fixed length. In the latter case there are two variants, one based on the full data, and another based on a sufficient statistic. We study the empirical performance of these estimators in three special cases, autoregressive (AR), moving average (MA) and fractionally differenced white noise (ARFIMA) models, and make comparisons with full and pairwise likelihood estimators. The results are somewhat model-dependent, with the new estimators doing well for MA and ARFIMA models, but less so for AR models.