Vector Autoregressive Moving Average Model with Scalar Moving Average

TL;DR

This paper introduces a method for estimating Vector Autoregressive Moving Average models with scalar moving average components using generalized least squares, simplifying the estimation process and connecting it to operator theory.

Contribution

It presents a novel estimation approach for VARMA models with scalar MA components using GLS, making the models more computationally accessible.

Findings

GLS can estimate VARMA models with scalar MA components efficiently.

The likelihood function resembles that of VAR models, facilitating optimization.

Connections to the Borodin-Okounkov formula in operator theory are discussed.

Abstract

We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynomial. The conditional variance of the GLS model is the concentrated covariant matrix of the moving average process. Under GLS the likelihood function of these models has similar format to their VAR counterparts. Maximum likelihood estimate can be done by optimizing with gradient over the moving average parameters. These models are inexpensive generalizations of Vector Autoregressive models. We discuss a relationship between this result and the Borodin-Okounkov formula in operator theory.