Statistical Inference for Autoregressive Models - with Random Coefficients and with Functional Realizations ; Statistische Inferenz für Autoregressive Modelle - mit zufälligen Koeffizienten und mit funktionalen Realisierungen
Titel:
Statistical Inference for Autoregressive Models - with Random Coefficients and with Functional Realizations ; Statistische Inferenz für Autoregressive Modelle - mit zufälligen Koeffizienten und mit funktionalen Realisierungen
Beteiligte:
Fink, Thorsten
[Verfasser:in]
Erschienen:
TU Braunschweig: LeoPARD - Publications And Research Data, 2013-04-05
Anmerkungen:
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Beschreibung:
In the first part we examine autoregressive (AR) processes with random coefficients. We propose a least-squares estimator for the fourth order moments of both the noise sequences and state its consistency. The main theme is the development of various bootstrap procedures for the distribution of the autoregressive parameter and the distribution of the variances of both noise sequences. We show how to obtain approximative residuals for the process even though the standard method for autoregressive processes does not work in this context since one then would obtain convoluted residuals of both the noise squences. These ideas lead to a modification of the classical residual bootstrap for autoregressive processes. The consistency of a bootstrap procedure for the autoregressive parameter based on an intuitive least-squares estimator as well as of a procedure based on a quasi maximum likelihood estimator, is established. Further, wild bootstrap modifications are proposed and the performances of the bootstrap procedures are explored by a simulation study and compared to each other. Finally, we propose two basic estimators and an advanced estimator that is based on deconvolution techniques for the densities of the noise sequences. In the second part we consider functional time series that are assumed to follow an autoregressive scheme of unknown order and show how to estimate this order consistently. We establish the connection between functional AR processes and multivariate AR processes and show how to obtain a multivariate process if we are given a functional AR process. We introduce a general loss function and show that the estimated order obtained by a minimization of this function converges to the correct order of the multivariate non-standard AR process and therefore of the functional AR process in probability. We evaluate the finite sample size performance by a simulation study and compare it with an existing method. Finally, we apply the method to real data sets. ; Im ersten Teil behandeln wir autoregressive ...