Search

In this paper we consider a regression model that allows for time series covariates as well as heteroscedasticity with a regression function that is modelled nonparametrically. We assume that the regression function changes at some unknown time ⌊ n s 0 ⌋ , s 0 ∈ (0 , 1) , and our aim is to estimate the (rescaled) change point s 0 . The considered estimator is based on a Kolmogorov-Smirnov functional of the marked empirical process of residuals. We show consistency of the estimator and prove a rate of convergence of O P (n - 1) which in this case is clearly optimal as there are only n points in the sequence. Additionally we investigate the case of lagged dependent covariates, that is, autoregression models with a change in the nonparametric (auto-) regression function and give a consistency result. The method of proof also allows for different kinds of functionals such that Cramér-von Mises type estimators can be considered similarly. The approach extends existing literature by allowing nonparametric models, time series data as well as heteroscedasticity. Finite sample simulations indicate the good performance of our estimator in regression as well as autoregression models and a real data example shows its applicability in practise. [ABSTRACT FROM AUTHOR]

Time reversibility is a fundamental hypothesis in time series. In this paper, Gini-based equivalents for time series concepts that enable to construct a Gini-based test for time reversibility under merely first-order moment assumptions are developed. The key idea is that the relationship between two variables using Gini (as measured by Gini autocorrelations and partial autocorrelations) can be measured in two directions, which are not necessarily equal. This implies a built-in capability to discriminate between looking at forward and backward directions in time series. The Gini creates two bi-directional Gini autocorrelations (and partial autocorrelations), looking forward and backward in time, which are not necessarily equal. The difference between them may assist in identifying models with underlying heavy-tailed and non-normal innovations. Gini-based test and Gini-based correlograms, which serve as visual tools to examine departures from the symmetry assumption, are constructed. Simulations are used to illustrate the suggested Gini-based framework and to validate the statistical test. An application to a real data set is presented. [ABSTRACT FROM AUTHOR]

It is known that the analysis of short panel time series data is very important in many practical problems. This paper calculates the exact moments up to order 4 under the null hypothesis of no serial correlation when there are many independent replications of size 3. We further calculate the tail probabilities under the null hypothesis using the Edgeworth approximation for $$n=3, 4$$ and $$5,$$ when the structure of the pdf (probability density function) of the test statistic is in essence different. Finally, we compare the three types of tail probabilities, namely, the Edgeworth approximation, the normal approximation and the exact probabilities through a large scale simulation study. [ABSTRACT FROM AUTHOR]