Bootstrap tests for simple structures in nonparametric time series regression.

This paper concerns statistical tests for simple structures such as parametric models, lower order models and additivity in a general nonparametric autoregression setting. We propose to use a modified L2-distance between the nonparametric estimator of regression function and its counterpart under null hypothesis as our test statistic which delimits the contribution from areas where data are sparse. The asymptotic properties of the test statistic are established, which indicates the test statistic is asymptotically equivalent to a quadratic form of innovations. A regression type resampling scheme (i.e. wild bootstrap) is adapted to estimate the distribution of this quadratic form. Further, we have shown that asymptotically this bootstrap distribution is indeed the distribution of the test statistics under null hypothesis. The proposed methodology has been illustrated by both simulation and application to German stock index data.

Baxter`s inequality and sieve bootstrap for random fields

The concept of the autoregressive (AR) sieve bootstrap is investigated for the case of spatial processes in Z2. This procedure fits AR models of increasing order to the given data and, via resampling of the residuals, generates bootstrap replicates of the sample. The paper explores the range of validity of this resampling procedure and provides a general check criterion which allows to decide whether the AR sieve bootstrap asymptotically works for a specific statistic of interest or not. The criterion may be applied to a large class of stationary spatial processes. As another major contribution of this paper, a weighted Baxter-inequality for spatial processes is provided. This result yields a rate of convergence for the finite predictor coefficients, i.e. the coefficients of finite-order AR model fits, towards the autoregressive coefficients which are inherent to the underlying process under mild conditions. The developed check criterion is applied to some particularly interesting statistics like sample autocorrelations and standardized sample variograms. A simulation study shows that the procedure performs very well compared to normal approximations as well as block bootstrap methods in finite samples

A model specification test for GARCH(1,1) processes

We provide a consistent specification test for GARCH(1,1) models based on a test statistic of Cramér-von Mises type. Since the limit distribution of the test statistic under the null hypothesis depends on unknown quantities in a complicated manner, we propose a model-based (semiparametric)bootstrap method to approximate critical values of the test and verify its asymptotic validity. Finally, we illuminate the finite sample behavior of the test by some simulations

The multiple hybrid bootstrap - resampling multivariate linear processes

Abstract. The paper reconsiders the autoregressive aided periodogram bootstrap (AAPB) which has been suggested i

Bootstrap Autoregressive Order Selection

In this paper we deal with the problem of fitting an autoregression of order p to given data coming from a stationary autoregressive process with infinite order. The paper is mainlyconcerned with the selection of an appropriate order of theautoregressive model. Based on the so-called final prediction error (FPE) a bootstrap order selection can be proposed, because it turns out that one relevant expression occuring in the FPE is ready for the application of the bootstrap principle. Some asymptotic properties of the bootstrap order selection are proved. To carry through the bootstrap procedure an autoregression with increasing but non-stochastic order is fitted to the given data. The paper is concluded by some simulations

Bootstrap of Kernel Smoothing in Nonlinear Time Series

Kernel smoothing in nonparametric autoregressive schemes offers a powerful tool in modelling time series. In this paper it is shown that the bootstrap can be used for estimating the distribution of kernel smoothers. This can be done by mimicking the stochastic nature of the whole process in the bootstrap resampling or by generating a simple regression model. Consistency of these bootstrap procedures will be shown

Evaluation of the benefits of vehicle safety technology: The MUNDS study

This paper was published in the journal, Accident Analysis and Prevention [© Elsevier Ltd.] and the definitive version is available at: http://dx.doi.org/10.1016/j.aap.2013.02.027Real-world retrospective evaluation of the safety benefits of new integrated safety technologies is hampered by the lack of sufficient data to assess early reliable benefits. This MUNDS study set out to examine if a “prospective” case-control meta-analysis had the potential to provide more rapid and rigorous analyses of vehicle and infrastructure safety improvements. To examine the validity of the approach, an analysis of the effectiveness of ESC using a consistent analytic strategy across 6 European and Australasian databases was undertaken. It was hypothesised that the approach would be valid if the results of the MUNDS analysis were consistent with those published earlier (this would confirm the suitability of the MUNDS approach). The findings confirm the hypothesis and also found stronger and more robust findings across the range of crash-types, road conditions, vehicle sizes and speed zones than previous. The study recommends that while a number of limitations were identified with the findings that need be addressed in future research, the MUNDS approach nevertheless should be adopted widely for the benefit of all vehicle occupants