Developments in Maximum Likelihood Unit Root Tests

Developments in Maximum Likelihood Unit Root Tests

The exact maximum likelihood estimate (MLE) provides a test statistic for the unit root test that is more powerful (Fuller, 1996, p. 577) than the usual least squares approach. In this paper a new derivation is given for the asymptotic distribution of this test statistic that is simpler and more direct than the previous method. The response surface regression method is used to obtain a fast alg...

Maximum Likelihood Estimation and Likelihood-ratio Tests

The method of maximum likelihood (ML), introduced by Fisher (1921), is widely used in human and quantitative genetics and we draw upon this approach throughout the book, especially in Chapters 13–16 (mixture distributions) and 26–27 (variance component estimation). Weir (1996) gives a useful introduction with genetic applications, while Kendall and Stuart (1979) and Edwards (1992) provide more ...

Bootstrap Unit Root Tests

We consider the bootstrap unit root tests based on finite order autoregressive integrated models driven by iid innovations, with or without deterministic time trends. A general methodology is developed to approximate asymptotic distributions for the models driven by integrated time series, and used to obtain asymptotic expansions for the Dickey–Fuller unit root tests. The second-order terms in ...

Differencing and Unit Root Tests

e d In the Box-Jenkins approach to analyzing time series, a key question is whether to difference th ata, i.e., to replace the raw data {y } by the differenced series {y −y }. Experience indicates that m t t t −1 ost economic time series tend to wander and are not stationary, but that differencing often yields a e r stationary result. A key example, which often provides a fairly good descriptio...

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