Markovian Representation and Existence Theorems for Bilinear Time Series Models
The Markovian representation (or state space form) plays an important role in the theory of linear time series models. Akaike (1974) has shown that the autoregressive — moving average model admits a linear Markovian representation and vice versa. A natural extension is to generalise the above results for the linear models to the bilinear models. It has been shown in section 5.2 that the bilinear model BL(p,0,p,1) given by (5.2.2) can be written in the vector form (5.2.4) and this in turn can be rewritten in terms of a Markovian representation. The general construction of Markovian representation for the bilinear models has been considered by Tuan Pham Dinh (1983), and here we briefly review his contribution.
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