Research Discussion Papers, Bank of Finland
No 26/2013:
Testing for a unit root in noncausal autoregressive models
Pentti Saikkonen ()
and Rickard Sandberg ()
Abstract: This work develops likelihood-based unit root tests in the
noncausal autoregressive (NCAR) model formulated by Lanne and Saikkonen
(2011, Journal of Time Series Econometrics 3, Iss. 3, Article 2). The
possible unit root is assumed to appear in the causal autoregressive
polynomial and for reasons of identification the error term of the model is
supposed to be non-Gaussian. In order to derive the tests, asymptotic
properties of the maximum likelihood estimators are established under the
unit root hypothesis. The limiting distributions of the proposed tests
depend on a nuisance parameter determined by the distribution of the error
term of the model. A simple procedure to handle this nuisance parameter
dependence in applications is proposed. Finite sample properties of the
tests are examined by means of Monte Carlo simulations. The results show
that the size properties of the tests are satisfactory and the power
against stationary NCAR alternatives is significantly higher than the power
of conventional Dickey-Fuller tests and the M-tests of Lucas (1995,
Econometric Theory 11, 331-346). In an empirical application to a Finnish
interest rate series evidence in favour of a stationary NCAR model with
leptokurtic errors is found.
Keywords: maximum likelihood estimation; noncausal autoregressive model; non-Gaussian time series; unit root; (follow links to similar papers)
JEL-Codes: C01; C12; C22; (follow links to similar papers)
29 pages, November 2, 2013
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