Abstract
This paper offers a perspective on testing unit root and other non-stationary hypotheses. We consider nested parametric hypothesis tests derived using the likelihood principle and examine why the limit behaviour of an estimator need not be uniformly asymptotically normal in an unknown parameter. We outline a role for information in explaining this result, relating the proof by Shiryaev and Spokoiny [11] in establishing a uniform limiting distribution for the autoregressive parameter in AR(1) models to the concept of “devolatization” of a time series [4]. This offers an interpretation of their method as regularizing the flow of Fisher information over time as a means of obtaining a uniform limiting normal result. We discuss hypothesis tests [2, 14] which are predicated on a more flexible view of non-stationarity and establish that the class of I(d) models is sufficiently flexible to permit a regular flow of Fisher information over time, supporting a uniform asymptotic theory and an attendant locally optimal statistical theory based on the chi-square distribution.
| Original language | English |
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| Title of host publication | 2003 Proceedings of the American Statistical Association, Information and Entropy Econometrics Conference in honour of Arnold Zellner |
| Pages | 286-289 |
| Publication status | Published - 2003 |
Keywords
- Unit root; non-stationary hypotheses; Fisher information; uniform asymptotic normality;