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Log-linear Poisson autoregression

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>03/2011
<mark>Journal</mark>Journal of Multivariate Analysis
Issue number3
Volume102
Number of pages16
Pages (from-to)563-578
Publication statusPublished
Early online date25/11/10
Original languageEnglish

Abstract

We consider a log-linear model for time series of counts. This type of model provides a framework where both negative and positive association can be taken into account. In addition time dependent covariates are accommodated in a straightforward way. We study its probabilistic properties and maximum likelihood estimation. It is shown that a perturbed version of the process is geometrically ergodic, and, under some conditions, it approaches the non-perturbed version. In addition, it is proved that the maximum likelihood estimator of the vector of unknown parameters is asymptotically normal with a covariance matrix that can be consistently estimated. The results are based on minimal assumptions and can be extended to the case of log-linear regression with continuous exogenous variables. The theory is applied to aggregated financial transaction time series. In particular, we discover positive association between the number of transactions and the volatility process of a certain stock.