The Hyvärinen scoring rule in Gaussian linear time series models

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