Hypothesis testing in a nearly integrated autoregressive model
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2012
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Melbourne Authors
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Dept. of Economics
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PhD thesis
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Manzoor, M. S. (2012). Hypothesis testing in a nearly integrated autoregressive model. PhD thesis, Dept. of Economics, The University of Melbourne.
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© 2012 Dr. Muhammad Saqib Manzoor
Abstract
In this dissertation, we revisit the method of Elliott and Stock (2001) to construct confidence intervals for an autoregressive coefficient by inverting a sequence of invariant point optimal tests. We show that the power properties of the point optimal tests can vary greatly with the choice of the point under the alternative at which power is maximised. Some choices are shown to lead to inconsistent tests, including, in some cases, the rule of thumb proposed by Elliott, Rothenberg, and Stock (1996). We propose the optimisation of a weighted power criterion as an alternative method to specify the point optimal tests and demonstrate that this provides tests with desirable asymptotic local power properties. We extend their method to t-tests and analyse in detail the finite and large sample power properties of these tests. We provide an alternative set of optimal values of model parameters to produce t-tests as powerful as the point optimal tests when testing for mildly explosive roots. The method is further extended to analyse the role of uncertainty about the initial condition on the size and power properties of the point optimal tests and t-tests. These uncertainties produce severe size distortions in the tests under consideration. We use the point optimal invariant test of Elliott and Muller (2006), but impose invariance to the initial condition under the null instead of the alternative to overcome this size issue. We observe that imposition of extra invariance when, indeed, it is not required results in power loss that escalates for mildly explosive roots. Asymptotic powers for different tests are also analysed for various values of the initial observation. We find that the point optimal invariant test, and the t_GLS test with this invariance imposed produce identical powers but perform poorly compared to t_OLS test.
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local-to-unity framework, autoregressive model, confidence interval construction, initial condition uncertainty, weighted average power maximisation, explosive autoregressive root, invariant Jeffreys prior, point optimal test, t-GLS test.