Essays on Testing for Smooth Structural Changes in Time Series
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This dissertation contains two essays which propose tests for smooth structural changes in dependence and volatility, respectively. In the first essay, we propose a generalized likelihood ratio test for smooth structural changes in copula parameters. Dependence between different financial assets plays a crucial role in many financial applications. The dependence structure is likely to change over time and the copula parameter also changes accordingly. Modeling the time varying nature of the copula parameter has drawn increased attention in the last decade because it has become increasingly recognized that dependence of financial assets is time-varying. In this essay, we consider the problem of testing for the time-varying copula parameter by the generalized likelihood ratio test based on the local maximum likelihood estimator. We derive the asymptotic null distribution of the proposed test. The finite sample performance of the test is illustrated by simulations and an empirical application is provided. In the second essay, we propose a generalized Hausman test for smooth structural changes in volatility. Since volatility is central to the financial theory and its empirical applications, there is a growing interest to analyze variance stability in financial markets, and the stylized facts of financial returns like IGARCH effects or variance persistence can be well explained by structural changes in the unconditional variance. The proposed test can be viewed as a generalized Hausman's (1978) test by comparing the local linear smoothing estimator, which is an inefficient but consistent estimator under HA, of volatility with the constrained estimator which is an efficient estimator under H0. We show that the new test is more powerful than the CUSUM test which has been mostly used to test for structural changes in volatility.
Yao, Hsin-Hung (2016). Essays on Testing for Smooth Structural Changes in Time Series. Doctoral dissertation, Texas A & M University. Available electronically from