Conditional Maximum Likelihood Estimation of Higher-Order Integer-Valued Autoregressive Processes
In this paper, we extend earlier work of Freeland and McCabe (2004) and develop a general framework for maximum likelihood (ML) estimation of higher-order integer-valued autoregressive (INAR(p)) processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is Binomial. A recursive representation of the transition probability for the INAR(p) model is proposed. Based on this representation, we derive expressions for the score function and the Fisher information matrix of the INAR(p) model, which form the basis for maximum likelihood estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. These new expressions enhance the interpretation of these quantities and lead naturally to new de?nitions for residuals for the INAR(p) model. Using the INAR(2) speci?cation with Poisson innovations, we examine the asymptotic effciency gain of implementing the ML technique over the widely used conditional least squares (CLS) method. We conclude that, if the Poisson assumption can be justified, there are substantial gains to be had from using ML especially when the thinning parameters are large.
|Date of creation:||2006|
|Date of revision:|
|Contact details of provider:|| Postal: Management School University of Liverpool, Chatham Street, Liverpool, L69 7ZH, Great Britain|
Phone: +44(0)151 795 3108
Fax: +44(0)151 795 3004
Web page: http://www.liv.ac.uk/management/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, 09.
- Jung, Robert C. & Tremayne, A.R., 2006. "Coherent forecasting in integer time series models," International Journal of Forecasting, Elsevier, vol. 22(2), pages 223-238.
When requesting a correction, please mention this item's handle: RePEc:liv:livedp:200619. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Simon Blackman)
If references are entirely missing, you can add them using this form.