Testing Hypothesis Methods
Historically speaking, the hypothesis testing methods had been dominantly used to choose tentative ARMA models until Box-Jenkins’ identification method appeared. Nowadays they are primarily used for testing model inadequacy after choosing the orders and estimating the parameters, which Box and Jenkins (1976) called the model diagnostic checking. Therefore, we discuss them in this final chapter.
KeywordsLagrange Multiplier Likelihood Ratio Test Statistic Lagrange Multiplier Test ARMA Process Test Hypothesis Method
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- (Section 6.1)For more details about the Wald, the LR, and the LM tests, readers may refer to Breusch and Pagan (1980), Berndt and Savin (1977), Engle (1984), and the references therein.Google Scholar
- (Section 6.2)About the singularity problem of overparameteriza- tion of the ARMA model, refer to Godfrey (1978a), Breusch (1978), Shibata (1986), and Veres (1987). Poskitt and TYemayne (1980) presented a ridge-regression type LM test of Ho against HC.Google Scholar
- (Section 6.2)For ARMA modeling methods utilizing Kolmogorov’s identity, refer to Cameron (1978), Milhoj (1981), Saikkonen (1983), Pham (1986, 1987), and the references therein.Google Scholar
- (Section 6.3)About the performance of the Qm and the Qm statistics, refer to Prothero and Wallis (1976), Davies and Newbold (1979), Ansley and Newbold (1979), Godolphin (1980b), and Clarke and Godolphin (1982).Google Scholar
- (Section 6.3)The equivalence of the portmanteau statistic and the LM statistic is also shown by Newbold (1980) and Poskitt and TVemayne (1981b, 1982).Google Scholar