Testing for and dating structural change in econometric models and nonparametric methods in financ

This thesis consists of four chapters. Chapter 1 and Chapter 2 are concerned with testing for and dating an unknown change point in semiparametric econometric models. Chapter 3 and Chapter 4 focus on using nonparametric methods to test, design and estimate multivariate continuous-time financial models.;In chapter 1, we propose a test for structural change with an unknown change point in semiparametric econometric models. The test statistic is a Sup Wald-type test statistic and extends Andrews's work (1993) by allowing an infinite dimensional parameter to enter the model. Therefore the test can be used to test parameter constancy and structural stability in a wide variety of semiparametric econometric models. A Monte Carlo experiment shows that the proposed test performs well in partially linear regression models.;In chapter 2, we develop an estimation procedure for a change point, occurring at an unknown date in partially linear time series models. The change point is estimated by maximizing a sequence of distances between pre-shift and post-shift estimated regression parameters of the model. The rate of convergence for the estimated change point is derived both for fixed magnitudes of the shifts and for shifts with magnitudes converging to zero as the sample size increases. Asymptotic distributions are also obtained for the estimated regression parameters.;In chapter 3, we extend the Ait-Sahalia's test (1996) of one factor continuous-time models to two-factor term structure models that have stationary marginal density functions. We study how the Ait-Sahalia's test and our extended test depend on the amount of smoothing applied to the data. It is found that the bias introduced in kernel density estimation has a significant influence on these tests. Consequently, in order to remove the influence of the bias, we propose a bias-corrected test statistic based on the idea of comparing the kernel density estimator and the kernel smoothing density function implied by the parametric model. In contrast, the bias-corrected test can be applied to any finite dimensional model. We then apply the extended test and bias-corrected test to test the specifications of two special cases, Brennan-Schwartz (1979) and Schaefer-Schwartz (1984) term structure models, of the affine class of term structure models developed by Duffie and Kan (1996).;In chapter 4, we propose a new two-factor model of the term structure that identifies the first factor with the spread, and the second factor with the console rate. To capture the true volatilities we impose no restrictions on the functional form of the volatility functions. We then develop a nonparametric procedure for estimating the volatility functions only on the discretely sampled observations. The asymptotic distributions of the proposed nonparametric estimators of volatility functions are also obtained. We implement the two-factor model by using Canadian term structure data. Nonparametric bond and bond option prices are computed and compared with those calculated under an alternative parametric model. The empirical results provide strong evidence that the traditional two-factor models are misspecified.