Comparisons of Hyv\"arinen and pairwise estimators in two simple linear time series models

TL;DR

This paper compares the performance of Hyv"arinen-based estimators with full and pairwise maximum likelihood estimators in AR(1) and MA(1) models through simulation studies, revealing distinct behaviors.

Contribution

It provides a numerical comparison of Hyv"arinen estimators against traditional likelihood methods in simple linear time series models, highlighting their differences.

Findings

Hyv"arinen estimators behave differently from pairwise likelihood estimators in AR(1) and MA(1) models.

Simulation results show contrasting performance patterns between the estimators.

The study offers insights into the suitability of different estimators for specific time series models.

Abstract

The aim of this paper is to compare numerically the performance of two estimators based on Hyv\"arinen'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 Hyv\"arinen scoring rule estimators relative to the pairwise likelihood estimators in these two settings.