Vector Autoregressive Moving Average Model with Scalar Moving Average

2019/09/01 by Du Nguyễn, Nguyen, Du
Computer Science · Mathematics · #37M10 #62M10 #91B84 #93C05 #FOS: Computer and information sciences #FOS: Economics and business #Matrix Theory and Algorithms #Methodology (stat.ME) #Random Matrices and Applications #Statistical Finance (q-fin.ST) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1909.00386

openalex publication_date 2019/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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