Book Description

This dissertation consists of three essays on specification tests on functional coefficient models via the Fourier transform and applications on conditional asset pricing models. The first essay, "An Asymptotically Efficient Test for Functional Coefficient Models", proposes a consistent test for model specification in a functional coefficient model that uses the discrete Fourier transform of a consistent nonparametric estimator of the random coefficient. As a generalization of the conditional moment tests by Bierens (1980, 1982), it is applicable in testing part of the coefficient functions, rather than testing for all of the them jointly. Although a nonparametric estimation step is included, my method is able to detect local alternatives at a rate of root T, owing to the U-process structure of the test statistics. Monte Carlo studies demonstrate that my method outperforms current nonparametric tests, such as the generalized likelihood ratio test by Fan et al. (2001) and the Wald-typed tests by Li et al. (2002), especially when the sample size decreases and the dimension of the state variables increases. In the second essay titled "A Consistent Model Specification Test for Functional Coefficient Models", I propose a consistent test for model specifications in functional coefficient models via discrete Fourier transform (DFT). The DFT of the sample score function can extract the local property of unknown parameters over the state variable. Therefore, my test avoids nonparametric estimation and is asymptotically more efficient than the existing nonparametric tests. It can detect a class of local alternatives at the parametric rate. Furthermore, my test allows the regressors and the state variables to be the same and is also robust to heteroscedasticity and serial correlation. Simulation studies show that the proposed test has reasonable size and excellent power against various misspecifications of coefficient functions. The two essays both aim at improving the efficiency of the tests over existing nonparametric tests in the literature. Rather than the same, they can be viewed as complement to each other. The first involves a step of nonparametric estimation and thus can test part of coefficient functions, rather than the joint test for all of the coefficient functions in the model. The drawback is that it is not tuning parameter free. The second uses a score function approach which is based on the residuals from the parametric estimation and is free of nonparametric estimation. Both have their merits and limitations and together provide a system of more efficient methods that can be applied in various economics circumstances. The third essay, "How Does Smooth Structural Change Affect Asymmetric Dependence in Foreign Exchange market?", I use a copula approach based on Patton (2006) to model this asymmetric exchange rate dependence and investigate how different but reasonable specification of marginal distribution affect the asymmetric behavior between mark-dollar and yen-dollar exchange rates. Central banks are facing a trade-off between export competitiveness and price stability, which will result in an asymmetric dependence behavior among currencies during joint appreciations versus during joint depreciation. It is plausible that the change pace of the underlying economic mechanism and technological progress can cause the structural change of exchange rate in a country. Furthermore, since the pattern of correlation or dependence structure is determined by second or higher order moment, we would expect the marginal structural change in volatility to change the dependence structure in joint distribution. This chapter can also serve as an empirical evidence of implementing smooth structural change into test for asymmetric correlations, proposed by Hong, Tu and Zhou (2007).