Essays on exponential series estimation and application of copulas in financial econometrics

This dissertation contains three essays. They are related to the exponential seriesestimation of copulas and the application of parametric copulas in financialeconometrics. Chapter II proposes a multivariate exponential series estimator (ESE) toestimate copula density nonparametrically. The ESE attains the optimal rate ofconvergence for nonparametric density. More importantly, it overcomes the boundarybias of copula estimation. Extensive Monte Carlo studies show the proposed estimatoroutperforms kernel and log-spline estimators in copula estimation. Discussion isprovided regarding application of the ESE copula to Asian stock returns during theAsian financial crisis. The ESE copula complements the existing nonparametric copulastudies by providing an alternative dedicated to the tail dependence measure.Chapter III proposes a likelihood ratio statistic using a nonparametric exponentialseries approach. The order of the series is selected by Bayesian Information Criterion(BIC). I propose three further modifications on my test statistic: 1) instead of puttingequal weight on the individual term of the exponential series, I consider geometric and exponential BIC average weights; 2) rather than using a nested sequence, I consider allsubsets to select the optimal terms in the exponential series; 3) I estimate the likelihoodratio statistic using the likelihood cross-validation. The extensive Monte Carlosimulations show that the proposed tests enjoy good finite sample performancescompared to the traditional methods such as the Anderson-Darling test. In addition, thisdata-driven method improves upon Neyman’s score test. I conclude that the exponentialseries likelihood ratio test can complement the Neyman’s score test.Chapter IV models and forecasts S&P500 index returns using the Copula-VARapproach. I compare the forecast performance of the Copula-VAR model with a classicalVAR model and a univariate time series model. I use this approach to forecast S&P500index returns. I apply a modified Diebold-Mariano test to test the equality of meansquared forecast errors and utilize a forecast encompassing test to evaluate forecasts. Thefindings suggest that allowing a more flexible specification in the error terms usingcopula tends improve the forecast accuracy. I also demonstrate combined forecastsimproved forecasts accuracy over individual models.