A test for model specification of diffusion processes

We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a Studentized $L_2$-distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process. To reduce the sensitivity of the test on smoothing bandwidth choice, the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths. To better capture the finite sample distribution of the test statistic and data dependence, the critical value of the test is obtained by a parametric bootstrap procedure. Properties of the test are evaluated asymptotically and numerically by simulation and by a real data example.Comment: Published in at http://dx.doi.org/10.1214/009053607000000659 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonparametric estimation and specification testing of a two-factor interest rate model

We propose a simple, flexible approach to nonparametric estimation and specification testing for a two-factor interest rate model. These methods are illustrated with a Monte Carlo experiment and an empirical example.Nonparametric local linear estimation, Two-factor term structure models, Model specification tests

Consistent nonparametric specification tests for stochastic volatility models based on the return distribution

This paper develops nonparametric specification tests for stochastic volatility models by comparing the nonparametically estimated return density and distribution functions with their parametric counterparts. Asymptotic null distributions of the tests are derived and the tests are shown to be consistent. Extensive Monte Carlo experiments are performed to study the finite sample properties of the tests. The tests are applied to an empirical dataset and we find the estimated stochastic volatility model is misspecified

Consistent nonparametric specification tests for stochastic volatility models based on the return distribution

This paper develops nonparametric specification tests for stochastic volatility models by comparing the nonparametically estimated return density and distribution functions with their parametric counterparts. Asymptotic null distributions of the tests are derived and the tests are shown to be consistent. Extensive Monte Carlo experiments are performed to study the finite sample properties of the tests. The proposed tests are applied in a number of empirical examples

Parameter estimation and model testing for Markov processes via conditional characteristic functions

Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for L\'{e}vy-driven processes. We propose an empirical likelihood approach, for both parameter estimation and model specification testing, based on the conditional characteristic function for processes with either continuous or discontinuous sample paths. Theoretical properties of the empirical likelihood estimator for parameters and a smoothed empirical likelihood ratio test for a parametric specification of the process are provided. Simulations and empirical case studies are carried out to confirm the effectiveness of the proposed estimator and test.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ400 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

A bootstrap test for the comparison of nonlinear time series - with application to interest rate modelling

We study the drift of stationary diffusion processes in a time series analysis of the autoregression function. A marked empirical process measures the difference between the nonparametric regression functions of two time series. We bootstrap the distribution of a Kolmogorov-Smirnov-type test statistic for two hypotheses: Equality of regression functions and shifted regression functions. Neither markovian behavior nor Brownian motion error of the processes are assumed. A detailed simulation study finds the size of the new test near the nominal level and a good power for a variety of parametric models. The two-sample result serves to test for mean reversion of the diffusion drift in several examples. The interest rates Euribor, Libor as well as T-Bond yields do not show that stylized feature often modelled for interest rates

A Likelihood Ratio Test of Stationarity Based on a Correlated Unobserved Components Model

We propose a likelihood ratio (LR) test of stationarity based on a widely-used correlated unobserved components model. We verify the asymptotic distribution and consistency of the LR test, while a bootstrap version of the test is at least first-order accurate. Given empirically-relevant processes estimated from macroeconomic data, Monte Carlo analysis reveals that the bootstrap version of the LR test has better small-sample size control and higher power than commonly used bootstrap Lagrange multiplier (LM) tests, even when the correct parametric structure is specified for the LM test. A key feature of our proposed LR test is its allowance for correlation between permanent and transitory movements in the time series under consideration, which increases the power of the test given the apparent presence of non-zero correlations for many macroeconomic variables. Based on the bootstrap LR test, and in some cases contrary to the bootstrap LM tests, we can reject trend stationarity for U.S. real GDP, the unemployment rate, consumer prices, and payroll employment in favor of nonstationary processes with volatile stochastic trends.Stationarity Test, Likelihood Ratio, Unobserved Components, Parametric Bootstrap, Monte Carlo Simulation, Small-Sample Inference

Nonparametric tests of the Markov hypothesis in continuous-time models

We propose several statistics to test the Markov hypothesis for $\beta$-mixing stationary processes sampled at discrete time intervals. Our tests are based on the Chapman--Kolmogorov equation. We establish the asymptotic null distributions of the proposed test statistics, showing that Wilks's phenomenon holds. We compute the power of the test and provide simulations to investigate the finite sample performance of the test statistics when the null model is a diffusion process, with alternatives consisting of models with a stochastic mean reversion level, stochastic volatility and jumps.Comment: Published in at http://dx.doi.org/10.1214/09-AOS763 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org