This paper develops a new framework and statistical tools to analyze stock returns using high-frequency data. We consider a continuous-time multifactor model via a continuous-time multivariate regression model incorporating realistic empirical features, such as persistent stochastic volatilities...

This paper proposes a statistical test of the martingale hypothesis. It can be used to test whether a given time series is a martingale process against certain non-martingale alternatives. The class of alternative processes against which our test has power is very general and it encompasses many...

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...