Modeling panels of intercorrelated autoregressive time series

We propose a method of modeling panel time series data with both inter- and intra-individual correlation, and of fitting an autoregressive model to such data. Estimates are obtained by a conditional likelihood argument. If there are few observations in each series, the estimates can be dramatically improved by Burg-type estimates 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 estimate, 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 estimate is of crucial importance.