Nichtparametrische Analyse und Prognose von Zeitreihen (Arbeiten zur Angewandten Statistik, 36) (German Edition),Used

Nichtparametrische Analyse und Prognose von Zeitreihen (Arbeiten zur Angewandten Statistik, 36) (German Edition),Used

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Any astronomer can predict just where every star will be at half past eleven tonight; he can make no such prediction about his daughter. James Truslow Adams, amerikanischer Historiker, 18781949 In der Zeitreihenanalyse spielt die Prognose zukiinftiger Werte eine wich tige Rolle. Je nach Anwendungsgebiet kann sie als Planungsund Steue rungshilfe, als Indikator von Fehlentwicklungen, zur Friiherkennung und Vorwarnung, aber auch zur Spekulation herangezogen werden. Dariiber hinaus ermoglichen die meisten Prognosetechniken das Ersetzen fehlender Werte innerhalb des Beobachtungszeitraumes. Statistische Vorhersagever fahren finden Verwendung in vielen wissenschaftlichen Disziplinen so beispielsweise in den Wirtschafts und Sozialwissenschaften, der Medizin, der Umweltforschung und der Hydrologie. Entstammen die beobachteten Zeitreihenwerte einem GauBprozeB, der durch Angabe seiner Mittelwertund Kovarianzfunktion charakterisiert ist, so geniigt es, die klassischen Verfahren anzuwenden. Hangen diese Funk tionen von endlich vielen Parametern ab, so konnen diese als Funktionen der Stichprobenautokovarianzen unter Regularitatsbedingungen asympto tisch effizient geschatzt werden. Die Prognosen sind dann zumeist lineare Funktionen der zuletzt beobachteten Zeitreihenwerte. Einleitung 2 Die Normalitatsannahme ist ftir Zeitreihendaten vor allem dann frag wiirdig, wenn der Verlauf der Reihe unregelmaf3ige Ausschlage aufweist, die sich von der Mehrzahl der Daten abheben. Wendet man ftir solche Zeitreihen dennoch ein auf der Normalitatsannahme beruhendes paramet risches Verfahren an, so verlieren die Schatzungen in aller Regel ihre Effi zienzeigenschaften. Da in der parametrischen Zeitreihenanalyse Prognosen iiblicherweise als Linearkombinationen einiger Werte vom Ende der Reihe berechnet werden, wobei die Schatzer als Koeffizienten eingehen, reduzie ren schlechte Parameterschatzungen im allgemeinen die Prognosegiite.

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