UC San Diego

The modeling of nonlinear and non-Gaussian dependence structures is of great interest to many researchers. Particularly, copula-based models have recently attracted a fair amount of attention due to their applicability and flexibility. This dissertation studies copula-based econometric models of intertemporal and cross-sectional dependence: the first and the third chapters analyze some general dependence types characterized by copulas, time irreversibility and stochastic monotonicity respectively. The second chapter focuses on the development of new copula-based models for stationary multivariate time series. The first chapter concerns a dependence property called time irreversibility. When we say a model is time irreversible, it means we may expect a plot of the series to exhibit different patterns when time runs forward and backward. We frequently observe time irreversibility in the asymmetric fluctuation of stock market data, unemployment rates, price series or business cycles. In the chapter we show that time reversibility is equivalent to the exchangeability of a copula function, and suggest a nonparametric test for time irreversibility. The distinguishing feature of our test is that it can detect any arbitrary form of irreversibility. We also show how time irreversible behavior may be described using a function called the circulation density, and propose a nonparametric estimator of this function. While my first project mainly concerned the first order stationary Markov chains of univariate time series, we turn our attention to higher dimensional cases in the second chapter. We show how to construct flexible models for multivariate time series using a graphical representation of joint distributions called vine copulas. Building on existing studies of copula-based univariate Markov models, our extension is made in two directions : (1) we consider multivariate time series, and (2) we allow Markov chains of any finite order. We propose a vine structure called the M-vine that is particularly well suited to model stationary Markov chains, and convenient to capture some interesting intertemporal and contemporary dependencies. An empirical application to the exchange rates of Korean won (KRW) and the Taiwanese dollar (TWD) is provided. In the last chapter, we study stochastic monotonicity, a dependence property that can be reframed in terms of the concavity of cross-sections of a copula function. Stochastic monotonicity is a distributional property which says that two variables tend to be positively associated, and it has been of great interest in many areas of economics such as experimental design, information economics, and labor economics. In this chapter, we discuss how to improve the power of the tests by using a modified bootstrap technique to choose a critical value that delivers a limiting rejection rate equal to nominal size over a wide region of the null hypothesis. To show the validity of this approach we draw on recent results on the directional differentiability of the least concave majorant operator, and on bootstrap inference when smoothness conditions sufficient to apply the functional delta method for the bootstrap are not satisfied