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Modellierung und Schätzung von ARMA-Prozessen

Modellierung und Schätzung von ARMA-Prozessen

          
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About the Book

Studienarbeit aus dem Jahr 2010 im Fachbereich VWL - Statistik und Methoden, Note: 1,0, Bayerische Julius-Maximilians-Universität Würzburg (Volkswirtschaftliches Institut), Veranstaltung: Zeitreihenanalyse, Sprache: Deutsch, Abstract: Die Seminararbeit "Modellierung und Schätzung von ARMA-Prozessen" bietet einen übersichtlichen Einstieg in stochastische Prozesse sowie ARMA-Prozesse als Methode zur Modellierung von Zeitreihen. Es werden zudem mehrere Schätzmethoden vorgestellt und miteinander verglichen. Heutzutage ist die Analyse von Zeitreihendaten in fast allen Wissenschaftsgebieten von großer Bedeutung, sei es in der Wirtschaft, in der Industrie, in der Demografie oder in Naturwissenschaften. Eine Zeitreihe kann als Realisation eines stochastischen Prozesses aufgefasst werden. Es wird angenommen, dass eine Familie von Zufallsvariablen des Prozesses eine bestimmte Verteilung besitzt und die Zufallsvariablen zu gewissen Wahrscheinlichkeiten Werte eines kontinuierlichen Intervalls annehmen. Wichtig für die Charakterisierung der stochastischen Prozesse sind die Momentfunktionen (Erwartungswert, Varianz, Autokovarianz, Autokorrelation). Durch Schätzer dieser Funktionen kann man auf den Prozess zurückschließen, der die Zeitreihe erzeugt hat. Dabei müssen bestimmte Voraussetzungen erfüllt sein, die unter den Begriffen "Stationarität" und "Ergodizität" zusammengefasst werden. In Kapitel 2 werden spezielle lineare Prozesse behandelt, die sich als Kombination von Zufallsvariablen und Schockterm ausdrücken lassen: White-Noise-Prozesse, autoregressive und Moving-Average-Prozesse sowie deren Kombination in ARMA-Prozessen. Dabei werden die Momentfunktionen der Prozesse hergeleitet sowie Invertierbarkeit und Kausalität erläutert. In Kapitel 3 wird in einer Einführung die Box-Jenkins-Methode als Ansatz zur Modellierung von Zeitreihen erklärt. In den folgenden Abschnitten werden drei Schätzer für die Parameter von ARMA-Prozessen vorgestellt: Yule-Walker-Schätzer, Maximum-Lik


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Product Details
  • ISBN-13: 9783640682959
  • Publisher: Grin Publishing
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 5 mm
  • Width: 148 mm
  • ISBN-10: 3640682955
  • Publisher Date: 21 Aug 2010
  • Height: 210 mm
  • No of Pages: 76
  • Series Title: German
  • Weight: 109 gr


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