We are interested in the stochastic properties, individual and joint, of mis- specification testing when the data are generated by an autoregressive process. Good mis-specification tests are invariant to the dynamic properties of the pro- cess summarized by its characteristic roots, and to irrelevant misspecifications. Invariance in parameter space obviates inference prior to mis-specification test- ing. This is important as the latter is used to validate the former. Mutual independence of the tests allows calibration of the overall significance level. Es- tablishing such results requires work on individual tests and on their stochastic interactions. In Chapter 2, we derive the asymptotic distribution of two types of CUSUM of squares test, one implemented with standardized one-step-ahead OLS pre- diction errors and another implemented with OLS residuals. The latter is found to be valid in all but singular explosive cases, but the former only in purely non-explosive, or regular explosive cases with all roots in the explosive region of the parameter space; in Chapter 3, we show that a nuisance term arises in the mixed case. In Chapter 4, we derive numerically a finite sam- ple correction to render the tests implementable into software, and Chapter 1 contains two examples of applications. In Chapter 5, we consider inference on the parameters associated with the stationary part of the process, together with tests for a unit root, lag length, variance constancy, and normality of the regression innovations. In character- izing the joint distribution of these tests, we rely on asymptotic theory, and show independence in the limit. A simulation experiment suggests that finite sample correlations between some of the tests are statistically significant but small. Asymptotically, then, control of the overall significance level of the test procedure is feasible, and there is no reason to discount inference for the use of these mis-specification tests in model selection.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:567932 |
| Date | January 2012 |
| Creators | Sohkanen, Jouni S. |
| Contributors | Nielsen, Bent |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:bc4abf3a-993c-4c69-9361-8debe538b696 |
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