TY - JOUR

T1 - Likelihood Estimation for the INAR(p) Model by Saddlepoint Approximation

AU - Pedeli, X.

AU - Davison, A.C.

AU - Fokianos, K.

PY - 2015

Y1 - 2015

N2 - Saddlepoint techniques have been used successfully in many applications, owing to the high accuracy with which they can approximate intractable densities and tail probabilities. This article concerns 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. The approach is applied to data on meningococcal disease counts. Supplementary materials for this article are available online.

AB - Saddlepoint techniques have been used successfully in many applications, owing to the high accuracy with which they can approximate intractable densities and tail probabilities. This article concerns 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. The approach is applied to data on meningococcal disease counts. Supplementary materials for this article are available online.

KW - INAR(p) model

KW - Maximum likelihood estimation

KW - Meningococcal disease

KW - Negative binomial distribution

KW - Poisson distribution

KW - Saddlepoint approximation

KW - Time series

U2 - 10.1080/01621459.2014.983230

DO - 10.1080/01621459.2014.983230

M3 - Journal article

VL - 110

SP - 1229

EP - 1238

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 511

ER -