AUEB SEMINARS - 17/12/2014: Likelihood estimation for the INAR(p) model by saddlepoint approximation

AUEB STATISTICS SEMINAR SERIES OCTOBER– DECEMBER 2014

Xanthi Penteli
Department of Statistics
Athens University of Economics and Business

Likelihood estimation for the INAR(p) model by saddlepoint approximation

Wednesday 17/12/2014
13:00 – 14:00

ROOM 607, 6th FLOOR,
POSTGRADUATE STUDIES BUILDING
(EVELPIDON & LEFKADOS)

ABSTRACT

Saddlepoint techniques have been used successfully in many applications, owing to the high accuracy with which they can approximate intractable densities and tail probabilities. We concern their use for the estimation of high-order integer-valued autoregressive, INAR(p), processes. Conditional least squares estimation and maximum likelihood estimation have been proposed for INAR(p) models, but the first is inefficient for estimating parametric models, and the second becomes difficult to implement as the order p increases. We propose a simple saddlepoint approximation to the log-likelihood that performs well even in the tails of the distribution and with complicated INAR models. We consider Poisson and negative binomial innovations, and show empirically that the estimator that maximises the saddlepoint approximation behaves very similarly to the maximum likelihood estimator in realistic settings.