University of Illinois Urbana-Champaign

Robust Testing for Unit Roots Based on Regression Rank Scores

Hasan, Mohammad Nazmul

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Description

Title
Robust Testing for Unit Roots Based on Regression Rank Scores
Author(s)
Hasan, Mohammad Nazmul
Issue Date
1993
Doctoral Committee Chair(s)
Koenker, Roger William,
Department of Study
Economics
Discipline
Economics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Statistics
  • Economics, Theory
Abstract
  • The objective of this thesis is to provide a robust statistical procedure for testing unit root models, based on regression-rank scores (RRS) introduced by Gutenbrunner and Jureckova (1990). These RRS arise as a vector of solutions of the dual form of the linear program required to compute the regression quantile statistics of Koenker and Bassett (1978). They are simple ranks of the sample observations for location model. To test the unit root of $y\sb{t}$, we consider the model$$\Delta y\sb{t}\equiv u\sb{t} = \mu + (\beta - 1)y\sb{t-1} + \sum\sbsp{j=1}{p}\phi\sb{j}u\sb{t-j} + e\sb{t}$$and test the null hypothesis, $(\beta-1)$ = 0, against local alternatives. In the finite variance case, the normal theory of our RRS based test statistics have the same rate of convergence 1/T, as the other existing tests based on least squares (LS) estimators, e.g. Dickey-Fuller (1979, 81), Phillips (1987), Phillips and Perron (1988). While their test statistics are complicated functionals of Brownian motion ours follow chi-square distribution asymptotically under both finite and infinite variance cases.
  • While the convergence rate for the LS estimator for infinite variance (Chan & Tran (1989), Phillips (1990)) remains 1/T, there is a substantial improvement if we use M-estimator which bound the influence of extreme innovations, since the rate of convergence is $a\sbsp{T}{-1}T\sp{-1/2}$, where $a\sb{T}=T\sp{1/\alpha}l(T)$ and $l(T)$ is a slowly varying function (Knight (1989)). Similar advantages are obtained for unit root testing since sequences of local alternatives may now be allowed to converge at rate $T\sp{-3/2}$ (for $\alpha$ = 1, Cauchy case), while least-squares based tests admit sequences of order $T\sp{-1}$. Unlike finite variance case, our test statistics require no nuisance parameter estimation in the infinite variance case. This fact distinguishes them from Wald and likelihood ratio type tests based on robust M-estimators as, for example, the $l\sb1$ tests of Herce (1990).
  • Finally, our proposed tests have more power than M-estimator based tests by choosing the optimal score function. However, in most cases, "Wilcoxon" score function is preferred since its asymptotic efficiency is bounded below by.86. This has been supported by an extensive monte carlo experiment.
Graduation Semester
1993
Type of Resource
text
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http://hdl.handle.net/2142/72423

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