On the use of wavelets in unit root and cointegration tests
Abstract: This thesis consists of four essays linked with the use of wavelet methodologies in unit root testing and in the estimation of the cointegrating parameters of bivariate models.In papers I and II, we examine the performance of some existing unit root tests in the presence of error distortions. We suggest wavelet-based unit root tests that have better size fidelity and size-adjusted power in the presence of conditional heteroscedasticity and additive measurement errors. We obtain the limiting distribution of the proposed test statistic in each case and examine the small sample performance of the tests using Monte Carlo simulations.In paper III, we suggest a wavelet-based filtering method to improve the small sample estimation of the cointegrating parameters of bivariate models. We show, using Monte Carlo simulations, that wavelet filtering reduces the small sample estimation bias.In paper IV, we propose a wavelet variance ratio unit root test for a system of equations. We obtain the limiting distributions of the test statistics under different specifications of the deterministic components of the estimating equations. We also investigate the small sample properties of the test by conducting Monte Carlo simulations. Results from the Monte Carlo simulations show that the test has good size fidelity for small sample sizes (of up to 100 observations per equation, and up to 10 equations), and has better size-adjusted power for these sample sizes, compared the Cross-sectionally Augmented Dickey-Fuller test.
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