The mathematical structure of error correction models

Abstract

The error correction model for a vector valued time series has been proposed and applied in the economic literature with the papers by Sargan (1964), Davidson et al. (1978), Hendry and von Ungern-Sternberg (1981) and has been given a formal mathematical treatment by Granger (1983). He introduced the notion of cointegratedness of a vector process and showed the relation between cointegration and error correction models. This paper defines a general error correction model, that encompasses the usual error correction model as well as the integral correction model by allowing a finite number of error correction terms which correspond to linear combinations of the vector process that are integrated of different order. It is shown that this structure is inherent in the model if it is given in autoregressive form or moving average form by exploiting the singularity of the matrix function that defines the model. The theory is applied to some examples discussed by Davidson (1983) and Harvey (1982). (Author)

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