Testing the Randomness of the Coefficients
As indicated in the previous chapter, the asymptotic results for the maximum likelihood estimates may be used to test certain hypotheses of interest. The condition (cii), however, which was assumed so as to obtain a standard central limit theorem for the maximum likelihood estimates, precludes the use of the theory derived in chapter 4 to test what is perhaps the most relevant hypothesis, namely that Σ = 0, that is, that the data come from a fixed coefficient autoregression. This chapter examines the testing of hypotheses in general, and in particular, two tests for the hypothesis that Σ = 0.
KeywordsCovariance Matrix Maximum Likelihood Estimate Symmetric Matrix Asymptotic Distribution Joint Density
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