Product Autoregressive Models: Review of Properties, Estimation Methods and Applications

Abstract

Analysis of continuous non-negative time series data using multiplicative models is a growing area of research. When the variable of interest is non-negative, often some methodology based on transformation was followed in the literature. Even though a useful class of models known as product autoregressive models was appeared in the literature long back, the further advancements happened only in the last decade. Through subsequent developments, it was shown that the product form of an additive autoregressive model is preferable to its linear counterpart when non-negativity has to be taken care. This paper aims to provide an exhaustive review of theoretical and empirical works conducted on product autoregressive models in the context of non-linear and non-Gaussian time series modelling. The notable properties, estimation methods and applications of these models are discussed followed by a description of some possible future research avenues on this area.