The Multiple Hybrid Bootstrap and Frequency Domain Testing for Periodic Stationarity ; Der multiple hybride Bootstrap und Testen auf periodische Stationarität im Spektralbereich
Titel:
The Multiple Hybrid Bootstrap and Frequency Domain Testing for Periodic Stationarity ; Der multiple hybride Bootstrap und Testen auf periodische Stationarität im Spektralbereich
Beteiligte:
Jentsch, Carsten
[Verfasser:in]
Erschienen:
TU Braunschweig: LeoPARD - Publications And Research Data, 2010-12-17
Anmerkungen:
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Beschreibung:
In the first part of this thesis, a new bootstrap procedure for dependent data is proposed and its properties are discussed. Under the assumption of a linear process, the idea of the autoregressive aided periodogram bootstrap (AAPB) of Kreiss and Paparoditis (2003) is reconsidered and in two directions generalized and complemented, respectively. On the one hand, the AAPB is modified in such a way that it is eventually able to generate bootstrap observations in the time domain, which is not possible for the AAPB. On the other hand, multivariate processes of arbitrary dimension are considered. It is shown that the multiple hybrid bootstrap (mHB) that includes the AAPB as a special case, is consistent under quite general assumptions for the sample mean and for kernel spectral density estimates. Moreover, for autocovariances and autocorrelations, different results between the univariate and the multivariate case are discussed. The second part deals with multivariate linear periodically stationary models, which generalize the usual stationary linear models in that effect that their coefficients are no longer assumed to be constant over time, but to behave periodically. These models may be represented as higher-dimensional stationary models and it is shown that their autocovariance structures as well as their spectral densities form upon specific patterns if and only if the underlying processes are actually not just periodically stationary, but also stationary. To test for stationarity, a test statistic based on nonparametric spectral density estimates is constructed that takes advantage of this specific shape. The asymptotic normal distribution of the test statistic is derived and it is shown that the test is asymptotically consistent. Moreover, it is demonstrated how to use the test statistic to test for periodic stationarity with shorter period. Finally, the mHB is used to obtain critical values that are more adequate than those from the CLT. ; Im ersten Teil wird ein neues Bootstrapverfahren für abhängige Daten ...