Econometrics

Download Applied Econometric Time Series (Wiley Series in Probability by Walter Enders PDF

By Walter Enders

Amstat information requested 3 evaluate editors to price their most sensible 5 favourite books within the September 2003 factor. utilized Econometric occasions sequence used to be between these selected. specific in that it covers sleek time sequence research from the only real prerequisite of an introductory path in a number of regression research. Describes the idea of distinction equations, demonstrating that they're the basis of all time-series types with emphasis at the Box-Jenkins technique. Considers many fresh advancements in time sequence research together with unit root exams, ARCH versions, cointegration/error-correction versions, vector autoregressions and extra. there are many examples to demonstrate a variety of strategies, a lot of which main issue econometric versions of transnational terrorism. The accompanying disk offers info for college kids to paintings with.

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Example text

XT ) im Inneren von Θ differenzierbar und liegt θ ˆ durch Lösen des Gleichungssystems von Θ, so wird man θ ∂ ln L (θ|x1 , . . , xT ) = 0, ∂θ1 .. ∂ ln L(θ|x1 , . . , xT ) = 0 ∂θr bestimmen. Eine einfache Anwendung wird im folgenden Abschnitt vorgestellt. Die Maximum-Likelihood-Methode hat einige günstige Eigenschaften. Eiˆ der ML-Schätzer für ne sehr nützliche Eigenschaft ist die Äquivarianz: Ist θ ˆ θ, so ist g(θ) der ML-Schätzer für g(θ). Manchmal interessiert man sich nicht für die Schätzung des Parameters θ selbst, sondern für die Schätzung einer Funktion g(θ) der Parameter.

2. 3 Maximum-Likelihood-Methode Wir gehen in diesem Abschnitt davon aus, dass die Verteilungsfunktion F von X bis auf einen r-dimensionalen Vektor von Parametern θ = (θ1 , . . , θ r ) ∈ Θ ⊂ Rr bekannt ist. Der Vektor θ ist zu schätzen. Die Maximum-LikelihoodMethode (ML-Methode) zur Herleitung von Schätzern ist zwar etwas komplizierter als die Methode der Momente, liefert aber in vielen Fällen (insbesondere für große Stichproben) Schätzer mit geringerer Varianz als die Methode der Momente. 13. Sei X Bernoulli-verteilt mit unbekanntem Parameter π; ferner sei X1 , .

XT ) = T t=1 f (xt ||θ) Durch den Doppelstrich soll verdeutlicht werden, dass es sich bei θ um einen Parametervektor (und nicht um gewöhnliche Funktionsargumente) handelt. 3 Parametrische Verteilungsmodelle 43 Der zweite Schritt besteht darin, die Likelihood-Funktion zu maximieren. Die ML-Schätzwerte ˆ θ1 , . . , ˆ θr für θ1 , . . , θ r sind definiert durch ˆ 1 , . . , xT ) = max L(θ|x1 , . . , xT ), L(θ|x θ∈Θ wobei wir die Existenz und Eindeutigkeit des Maximums in Θ stillschweiˆ ist es oft günstiger, gend voraussetzen.

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