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In this paper, we establish some new central limit theorems for generalized U-statistics of dependent processes under some mild conditions. Such central limit theorems complement existing existing results available from both the econometrics literature and statistics literature. We then look at applications of the established results to a number of test problems in time series regression models.

We propose two nonparametric transition density-based speciÞcation tests for continuous-time diffusion models. In contrast to marginal density as used in the literature, transition density can capture the full dynamics of a diffusion process, and in particular, can distinguish processes with the same marginal density but different transition densities. To address the concerns of the Þnite sample performance of nonparametric methods in the literature, we introduce an appropriate data transformation and correct the boundary bias of kernel estimators. As a result, our tests are robust to persistent dependence in data and provide reliable inferences for sample sizes often encountered in empirical Þnance. Simulation studies show that our tests have reasonable size and good power against a variety of alternatives in Þnite samples even for data with highly persistent dependence. Besides the single-factor diffusion models, our tests can be applied to a broad class of dynamic economic models, such as discrete time series models, time-inhomogeneous diffusion models, stochastic volatility models, jump-diffusion models, and multi-factor term structure models. When applied to daily Eurodollar interest rates, our tests overwhelmingly reject some popular spot rate models, including those with nonlinear drifts that some existing tests can not reject after correcting size distortions. We Þnd that models with nonlinear drifts do not signiÞcantly improve the goodness-of-Þt, and the main source of model inadequacy seems to be the violation of the Markov assumption. We also Þnd that GARCH, regime switching and jump diffusion models perform signiÞcantly better than single-factor diffusion models, although they are far from being adequate to fully capture the interest rate dynamics. Our study shows that nonparametric methods are a reliable and powerful tool for analyzing Þnancial data.

In the paper, we use a panel data approach to study the threshold effects and nonlinearity in economic growth instead of the cross-sectional approach commonly used in previous studies. The methodologies developed by Hansen (2000) and Caner and Hansen (2004) are applied to identify threshold variables. The analysis reveals many threshold variables, in particular for short lengths of panels. However, the results vary according to the number of observations included. To reduce the large number of potential threshold variables, principle component analyses are used to create a smaller number of composite factors and test the threshold effects. Using a five-year panel, we show how to classify countries into different growth typologies. Finally, a local linear nonparametric estimation method is presented to illustrate the nonlinear curves of convergence relative to the threshold variables.

Stock and Watson (1998 and 1999) developed a factor-model approach which allows for big data sets to be systematically reduced to a few explanatory factors. In this paper two other methods are proposed. The first one, Partial Least Squares is imported from the Chemometrics literature. The second one, which is based on the Combination of Forecasts literature is a modification of Stock and Watson’s method. We will call this method Principal Components Combination. These methods are compared in an empirical application to inflation. We conclude that the method with the best overall performance is the Principal Components Combination.

This paper gives a selective review on the recent developments of nonparametric methods in continuous-time finance, particularly in the areas of nonparametric estimation of diffusion processes, nonparametric testing of parametric diffusion models, and nonparametric pricing of derivatives. For each financial context, the paper discusses the suitable statistical concepts, models, and modeling procedures, as well as some of their applications to financial data. Their relative strengths and weakness are discussed. Much theoretical and empirical research is needed in this area, and more importantly, the paper points to several aspects that deserve further investigation.

This paper gives a selective review on the recent developments of nonparametric methods in continuous-time finance, particularly in the areas of nonparametric estimation of diffusion processes, nonparametric testing of parametric diffusion models, and nonparametric pricing of derivatives. For each financial context, the paper discusses the suitable statistical concepts, models, and modeling procedures, as well as some of their applications to financial data. Their relative strengths and weakness are discussed. Much theoretical and empirical research is needed in this area, and more importantly, the paper points to several aspects that deserve further investigation.

We propose two nonparametric transition density-based speciþcation tests for continuous-time diffusion models. In contrast to marginal density as used in the literature, transition density can capture the full dynamics of a diffusion process, and in particular, can distinguish processes with the same marginal density but different transition densities. To address the concerns of the þnite sample performance of nonparametric methods in the literature, we introduce an appropriate data transformation and correct the boundary bias of kernel estimators. As a result, our tests are robust to persistent dependence in data and provide reliable inferences for sample sizes often encountered in empirical þnance. Simulation studies show that our tests have reasonable size and good power against a variety of alternatives in þnite samples even for data with highly persistent dependence. Besides the single-factor diffusion models, our tests can be applied to a broad class of dynamic economic models, such as discrete time series models, time-inhomogeneous diffusion models, stochastic volatility models, jump-diffusion models, and multi-factor term structure models. When applied to daily Eurodollar interest rates, our tests overwhelmingly reject some popular spot rate models, including those with nonlinear drifts that some existing tests can not reject after correcting size distortions. We þnd that models with nonlinear drifts do not signiþcantly improve the goodness-of-þt, and the main source of model inadequacy seems to be the violation of the Markov assumption. We also þnd that GARCH, regime switching and jump diffusion models perform signiþcantly better than single-factor diffusion models, although they are far from being adequate to fully capture the interest rate dynamics. Our study shows that nonparametric methods are a reliable and powerful tool for analyzing þnancial data.