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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2451/28231
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| Title: | Bias Reduction and Likelihood Based Almost-Exactly Sized Hypothesis
Testing in Predestricted Likelihoodictive Regressions using the R |
| Authors: | Chen, Willa W.
Deo, Rohit S. |
| Keywords: | Bartlett correction
likelihood ratio test
curvature |
| Issue Date: | 24-Aug-2009 |
| Series/Report no.: | SOR-2009-06 |
| Abstract: | Difficulties with inference in predictive regressions are generally
attributed to strong persistence in the predictor series. We show that
the major source of the problem is actually the nuisance intercept
parameter and propose basing inference on the Restricted
Likelihood,which is free of such nuisance location parameters and also
possesses small curvature, making it suitable for inference. The bias of
the Restricted Maximum Likelihood (REML) estimates is shown to be
approximately 50% less than that of the OLS estimates near the unit
root, without loss of efficiency. The error in the chi-square
approximation to the distribution of the REML based Likelihood Ratio
Test (RLRT) for no predictability is shown to be 3/4 − ρ2
n−1 (G3 (·) − G1 (·)) + O n−2 ,
where |ρ| < 1 is the correlation of the innovation series and Gs
(·) is the c.d.f. of a χ2s random variable. This very small
error, free of the AR parameter, suggests that the RLRT for
predictability has very good size properties even when the regressor has
strong persistence. The Bartlett corrected RLRT achieves an O
n−2 error. Power under local alternatives is obtained and
extensions to more general univariate regressors and vector AR(1)
regressors, where OLS may no longer be asymptotically efficient, are
provided. In simulations the RLRT maintains size well, is robust to
non-normal errors and has uniformly higher power than the
Jansson-Moreira test with gains that can be substantial. The Campbell-
Yogo Bonferroni Q test is found to have size distortions and can be
significantly oversized. |
| URI: | http://hdl.handle.net/2451/28231 |
| Appears in Collections: | IOMS: Statistics Working Papers
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