Discussion Papers, Department of Business and Management Science, Norwegian School of Economics (NHH)
Treating missing values in INAR(1) models
() and Dimitris Karlis
Abstract: Time series models for count data have found increased
interest in recent days. The existing literature refers to the case of data
that have been fully observed. In the present paper, methods for estimating
the parameters of the first-order integer-valued autoregressive model in
the presence of missing data are proposed. The first method maximizes a
conditional likelihood constructed via the observed data based on the
k-step-ahead conditional distributions to account for the gaps in the data.
The second approach is based on an iterative scheme where missing values
are imputed in order to update the estimated parameters. The first method
is useful when the predictive distributions have simple forms. We derive in
full details this approach when the innovations are assumed to follow a
finite mixture of Poisson distributions. The second method is applicable
when there are not closed form expressions for the conditional likelihood
or they are hard to derive. Simulation results and comparisons of the
methods are reported. The proposed methods are applied to a data set
concerning syndromic surveillance during the Athens 2004 Olympic Games.
Keywords: Imputation; Markov Chain EM algorithm; mixed Poisson; discrete valued time series; (follow links to similar papers)
JEL-Codes: C32; (follow links to similar papers)
17 pages, August 13, 2008
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