PDF⋙ Bootstrapping Stationary ARMA-GARCH Models by Kenichi Shimizu

Bootstrapping Stationary ARMA-GARCH Models by Kenichi Shimizu

Bootstrapping Stationary ARMA-GARCH Models

Bootstrapping Stationary ARMA-GARCH Models by Kenichi Shimizu PDF, ePub eBook D0wnl0ad

Im Jahre 1979 hat Bradley Efron mit seiner Arbeit Bootstrap Methods: Another Look at the Jackknife das Tor zu einem in den vergangenen 30 Jahren intensiv bearbeiteten Forschungsgebiet aufgestossen. Die simulationsbasierte Methode des Bootstraps hat sich in den verschiedensten Bereichen als ein ausserordentlich - ?zientes Werkzeug zur Approximation der stochastischen Fluktuation eines Sch- zers um die zu schatzende Grosse erwiesen. Prazise Kenntnis dieser stochastischen Fluktuation ist zum Beispiel notwendig, um Kon?denzbereiche fur Schatzer an- geben, die die unbekannte interessierende Grosse mit einer vorgegebenen Wa- scheinlichkeit von, sagen wir, 95 oder 99% enthalten. In vielen Fallen und bei korrekter Anwendung ist das Bootstrapverfahren dabei der konkurrierenden und auf der Approximation durch eine Normalverteilung basierenden Methode ub- legen. Die Anzahl der Publikationen im Bereich des Bootstraps ist seit 1979 in einem atemberaubenden Tempo angestiegen. Die wesentliche und im Grunde e- fache Idee des Bootstraps ist die Erzeugung vieler (Pseudo-) Datensatze, die von ihrer wesentlichen stochastischen Struktur dem Ausgangsdatensatz moglichst a- lich sind. Die aktuellen Forschungsinteressen im Umfeld des Bootstraps bewegen sich zu einem grossen Teil im Bereich der stochastischen Prozesse. Hier stellt sich die zusatzliche Herausforderung, bei der Erzeugung die Abhangigkeitsstruktur der Ausgangsdaten adaquat zu imitieren. Dabei ist eine prazise Analyse der zugrunde liegenden Situation notwendig, um beurteilen zu konnen, welche Abhangigkei- aspekte fur das Verhalten der Schatzer wesentlich sind und welche nicht, um a- reichend komplexe, aber eben auch moglichst einfache Resamplingvorschlage fur die Erzeugung der Bootstrapdaten entwickeln zu ko

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