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Biometrika 1999 86(3):573-590; doi:10.1093/biomet/86.3.573
© 1999 by Biometrika Trust
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Modelling panels of intercorrelated autoregressive time series

V HjellvikA1 and D TjøA2

A1 Institute of Marine Research, Postbox 1870, Nordnes, 5024 Bergen, Norway E-mail: vidar.hjellvik@imr.no A2 Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway E-mail: dag.tjoshteim@mi.uib.no

We propose a method of modelling panel time series data with both inter- and intra-individual correlation, and of fitting an autoregressive model to such data. Estimators are obtained by a conditional likelihood argument. If there are few observations in each series, the estimators can be dramatically improved by Burg-type estimators taking edge effects into account. The consequences of ignoring the intercorrelation term are analysed. Partial lack of consistency is demonstrated in this situation. Moreover, a break-even point is found for the strength of the intercorrelation, beyond which a conventional estimator, ignoring correlation, will become increasingly inferior. Asymptotic normality of estimators is established, and our results are illustrated on a real data example, where it is seen that choosing the right type of estimator is crucial.

Key Words: Autoregressive; Burg-type estimator; Intercorrelated; Panel data; Time series


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