SeleccionModelos.pdf - Seleccin de Modelos 1 Criterios de...

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Selecci°n de Modelos 1 Criterios de Informaci°n ¿C°mo seleccionar un modelo de entre varios candidatos? V±a Criterios de Infor- maci°n. Aqu± se describen tres criterios: AIC (Akaike Information Criterium), BIC (Bayesian Criterium y HQ (Hannan-Quin). Supongamos que tenemos ° k modelos alternativos M 1 , M 2 ,..., M k ,..., M ° k , donde k representa el noemero de parÆmetros que tiene el modelo M k . Segoen los cr±terios de informaci°n se elige " k " tal que minimice IC ( k ) = ln ^ ° 2 k + k C ( T ) T donde ^ ° 2 k es la varianza residual del modelo M k , T es el tamaæo muestral y C ( T ) es un tØrmino de penalizaci°n (o "penalty") que var±a en funci°n del criterio de informaci°n seleccionado. El AIC especi²ca C ( T ) = 2 , el BIC C ( T ) = ln T y el HQ C ( T ) = 2 ° ln(ln T ) . 1
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2 Modelos ARMA Si se elige entre modelos de tipo AR(p), k = p ; y si se escoge entre modelos de tipo ARMA(p,q) k = p + q . Supongamos que estamos eligiendo entre la familia de modelos AR(p). ^ p ( IC ) se elige tal que IC (^ p ( IC )) = min f IC ( p ) j p = 0 ; 1 ; :::; ° k g : Un estimador ^ p
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