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 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 bootstrap test for the comparison of nonlinear time series

The difference between the regression functions of two stationary conditional heteroskedastic autoregressive time series is tested. The functions can be equal, or shifted, under the null hypothesis. Local linear estimation of the regression function results in observable residuals. Bootstrap residuals lead to a marked empirical process as test statistic and a Kolmogorov-Smirnov version is applied. The simulation study for linear, exponential or trigonometric regression functions with homoskedastic or heteroskedastic errors finds the rejection probability under the null hypothesis to be near the level. Comparing series with different combinations of linear, exponential and trigonometric functions, the rejection probability under the alternative yields mixed results.