Many time series observed in practice indicate various nonstationarities that can arise in various ways. We focus on the trend in mean.

The considered problem is formulated in the framework of detecting structural breaks in trending and possibly dynamic regression models in which the regressors are generated by suitably smooth (random) functions. The proposed test procedures are related to likelihood ratio type statistics and statistics based on partial sums of weighted residuals. Limit behavior of the proposed test procedures both under no change and at least one change is studied. The main theoretical result of the paper establishes the extreme value distribution of these statistics. This provides a simple approximation for the needed critical values. However it appears that the convergence to the extreme value limit is rather slow therefore a suitable version of the circular bootstrap is proposed and then applied.

Theoretical results are accompanied by a simulation study and an application to air carrier traffic data. The finite sample performance is satisfactory.

References:

Aue, A., Horvath, L., Huskova, M., and Kokoszka, P. (2008). Testing for changes in polynomial regression. Bernoulli 14, 637-660.

Aue, A., Horvath, L., Huskova, M.(2010) Segmenting mean-nonstationary time series via trending regressions, submitted.

Wu, W.B., and Zhao, Z. (2007). Inference of trends in time series. Journal of the Royal Statistical Society, Series B 69, 391-410.

Keywords: time series; trending regression; structural breaks; extreme value asymptotics

Biography: Working at Charles University in Prague. Areas of research interest: change point problem, asymptotic statistics, sequential statistical analysis, nonparametric statistics. Member of the editorial boards of 4 statistical journals. Also active in various statistical societies, at this moment the member of the council of the ISI.