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Title:  Robust Testing for Unit Roots Based on Regression Rank Scores 
Author(s):  Hasan, Mohammad Nazmul 
Doctoral Committee Chair(s):  Koenker, Roger William, 
Department / Program:  Economics 
Discipline:  Economics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Statistics
Economics, Theory 
Abstract:  The objective of this thesis is to provide a robust statistical procedure for testing unit root models, based on regressionrank 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$$\Delta y\sb{t}\equiv u\sb{t} = \mu + (\beta  1)y\sb{t1} + \sum\sbsp{j=1}{p}\phi\sb{j}u\sb{tj} + e\sb{t}$$and test the null hypothesis, $(\beta1)$ = 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. DickeyFuller (1979, 81), Phillips (1987), Phillips and Perron (1988). While their test statistics are complicated functionals of Brownian motion ours follow chisquare 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 Mestimator 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 leastsquares 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 Mestimators as, for example, the $l\sb1$ tests of Herce (1990). Finally, our proposed tests have more power than Mestimator 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. 
Issue Date:  1993 
Type:  Text 
Description:  195 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1993. 
URI:  http://hdl.handle.net/2142/72423 
Other Identifier(s):  (UMI)AAI9411647 
Date Available in IDEALS:  20141217 
Date Deposited:  1993 
This item appears in the following Collection(s)

Dissertations and Theses  Economics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois