In the first chapter; we consider nonlinear transformations of random walks driven by thick-tailed innovations with infinite means or variances. In particular, we show how nonlinearity, nonstationarity, and thick tails interact to generate persistency in memory, and we clearly demonstrate that...

In Chapter 1, I develop a test for the martingale hypothesis using the fact that a continuous martingale is time-deformed browninan motion, where the deforming process is quadratic variation of the martingale. Sampling a martingale at equal increases in quadratic variation and taking first...

We consider a volatility model, named ARCH-NNH model, that is specifically an ARCH process with a nonlinear function of a persistent, integrated or nearly integrated, explanatory variable.We first establish the asymptotic theories showing that the time series properties of our model successfully...

We present three essays on the econometric modeling of time-varying densities. In all three studies, we treat density functions themselves as random elements taking values in the Hilbert space of square integrable functions. The first essay introduces functional autoregression of one sequence of...

We consider the stochastic volatility model with smooth transition and persistent la-tent factors. We argue that this model has advantages over the conventional stochasticmodel for the persistent volatility factor. Though the linear filtering is widely usedin the state space model, the...

I consider continuous time asset pricing models with stochastic differential utilityincorporating decision makers' concern with ambiguity on true probability measure.In order to identify and estimate key parameters in the models, I use a novel econometricmethodology developed recently by Park...

This dissertation collects two papers regarding the econometric and economic theoryand testing of the predictability of asset returns. It is widely accepted that stockreturns are not only predictable but highly so. This belief is due to an abundanceof existing empirical literature fi nding often...

In this paper I derive the asymptotics of the exact, Euler, and Milstein MLestimators for diffusion models, including general nonstationary diffusions. Thoughthere have been many estimators for the diffusion model, their asymptotic propertieswere generally unknown. This is especially true for...

U.S. Treasury Securities are crucially important in many areas of finance. However, zero-coupon yields are not observable in the market. Even though published zero-coupon yields exist, they are sometimes not available for certain research topics or for high frequency. Recently, high frequency...

A recursive test procedure is suggested that provides a mechanism for testing explosive behavior, date-stamping the origination and collapse of economic exuberance, and providing valid confidence intervals for explosive growth rates. The method involves the recursive implementation of a...