| In this thesis, we present a series of projects on stationarity, volatility, and contagion in continuous- and discrete-time financial models.;In the first chapter, we present a hypothesis testing procedure involving a single sample path from a continuous, univariate stochastic differential equation. This sample path is used to compute two different nonparametric estimators of the diffusion function, one temporal and one spatial. These estimators are used to check whether it is likely that the diffusion function is time inhomogeneous (which, in turn, implies that the diffusion is not stationary). We apply the testing procedure to exchange rates and interest rates, two types of financial time series that are often modeled by stationary diffusions.;In the next two chapters, we turn to a discrete-time context and address the ongoing debate as to whether or not there is contagion in fixed income markets. Using a nonlinear regression model and associated local correlation function, we say there is contagion from a financial market X to Y if there is greater dependence between X and Y when X is experiencing a crisis than when X is more "normal." Also, we define a concept called confusion, which occurs when the local correlation not only decreases from the median to a tail of X, but does so to the extent that it is statistically indistinguishable from zero in the tail. We develop a related bootstrapping technique and use it to find evidence that bond markets and credit default swap markets seem to be free of contagion, but occasionally subject to confusion.;In the final chapter, we develop a generalization of the Durbin-Watson test statistic for a nonlinear regression model. This generalization is called the local Durbin-Watson function. We propose a permutation testing procedure which, when combined with a multiple comparisons procedure, determines whether or not an estimate of the local Durbin-Watson function indicates the presence of local autocorrelation somewhere along the distribution of the covariate. |
