Browsing by Author "David A. Dickey, Committee Co-Chair"

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    Inference Regarding Multiple Structural Changes in Linear Models Estimated via Two Stage Least Squares.
    (2005-12-28) Han, Sanggohn; Alastair R. Hall, Committee Chair; David A. Dickey, Committee Co-Chair; Sastry G. Pantula, Committee Member; Atsushi Inoue, Committee Member
    Bai and Perron(1998) develop methods that are designed to test for structural stability with an unknown number of break points in the sample. Their analysis is in the context of linear regression models estimated via Ordinary Least Squares(OLS). We extend Bai and Perron's framework for multiple break testing to linear models via Two Stage Least Squares(2SLS). Within our framework, the break points are estimated simultaneously with the regression parameters via minimization of the residual sum of squares on the second step of the 2SLS estimation. We establish the consistency of the resulting estimated break point fractions and obtain the standard convergence rate of break fraction estimators. Based on that convergence rate we derive the limiting distribution of the break point estimators. We prove that the break point estimator have the same limiting distribution of the arg max of two sided Brownian motion process, which is the same distribution considered by Bai and Perron(1998). We also show that various F-statistics for structural instability based on the 2SLS estimator have the same limiting distribution as the analogous statistics for OLS considered by Bai and Perron(1998). This allows us to extend Bai and Perron's(1998) sequential procedure for selecting the number of break points to the 2SLS setting. Simulation experiment and application to financial market has been implemented.
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    Seasonal Unit Root Tests: A Comparison
    (2008-10-26) Zhang, Qianyi; Denis Pelletier, Committee Member; Peter Bloomfield, Committee Member; Sastry G. Pantula, Committee Co-Chair; David A. Dickey, Committee Co-Chair
    Three major regression-based seasonal unit root tests: the DHF test introduced by Dickey et al (1984), the HEGY test proposed by Hylleberg et al. (1990) and the Kunst test introduced by Kunst (1997) are compared. The regression model for the DHF test is a reduced form of that for the Kunst test. We modify the Kunst test by using the t-statistic instead of Kunst's proposed joint F-statistic to study the influence of additional variables in the Kunst model. Also, we modify the HEGY test to test the presence of all four quarterly unit roots against the presence of roots 1 and -1. Through the comparison between the DHF test and the modified HEGY test, we find that the DHF test does not have asymptotic power one when the series only have some of the seasonal unit roots but not all of them. We call this case of partial unit roots. The asymptotic distributions derived in the paper provide the explanation of this limitation for the DHF test. Using simulation, we find that the probability that the DHF test will lead researchers to accept the seasonal unit root null hypothesis increases when the series contains more partial unit roots. For the DHF test, the test power depends on the augmented model. We derive limits of the related estimates from two augmented models for the DHF test. Both estimates are inconsistent. The test statistic obtained from the augmented model suggested by Ghysels et al. (1992) has relatively low power. For the HEGY/Kunst test, most limiting distributions for the test statistics depend on the lag augmentation but the test statistics have few problems caused by inconsistent estimates. However, the augmented models for the HEGY/Kunst test have more variables than those for the DHF test. Based on our simulation study results, the inclusion of more variables results in more loss in power when a redundant variable is included, and more sensitivity to the size distortion when the augmented lag length is less than the true lag length.