Estimating weak periodic vector autoregressive time series

TL;DR

This paper derives the asymptotic distribution of least squares estimators in periodic vector autoregressive models with dependent innovations, proposing modified Wald tests and illustrating results through simulations and financial data application.

Contribution

It provides new asymptotic distribution results for PVAR models with dependent innovations and introduces modified Wald tests for linear restrictions.

Findings

Asymptotic distributions differ when innovations are dependent.

Modified Wald tests improve hypothesis testing in PVAR models.

Monte Carlo experiments validate theoretical results.

Abstract

This article develops the asymptotic distribution of the least squares estimator of the model parameters in periodicvector autoregressive time series models (hereafter PVAR) with uncorrelated but dependent innovations. When theinnovations are dependent, this asymptotic distributions can be quite different from that of PVAR models with in-dependent and identically distributed (iid for short) innovations developed in Ursu and Duchesne (2009). Modifiedversions of the Wald tests are proposed for testing linear restrictions on the parameters. These asymptotic results are illustrated by Monte Carlo experiments. An application to a bivariate real financial data is also proposed