Parameter Estimation in Panels of Intercorrelated Time Series

Abstract

We consider parameter estimation in panels of intercorrelated time series. By a factorisation of the conditional log-likelihood function we obtain a new estimator \hat{a}_n,T for panels of intercorrelated autoregressive time series. We generalise this model to a factor model, where a single underlying background process is responsible for the common behaviour of the time series in the panel, and derive the corresponding conditional maximum likelihood estimators. Consistency and asymptotic normality are proved for the estimators in both models. It turns out that \hat{a}_n,T is asymptotically equivalent to the estimator \hat{a}_HT given in Hjellvik and Tjostheim (1999a) if the number of time series in the panel tends to infinity. It is more efficient if only the length of the time series increases. Furthermore the mean squared errors of the dominant terms in the stochastic expansions of these estimators have the ratio (n-1)/n, which indicates that already the small sample bias of \hat{a}_n,T is smaller than that of \hat{a}_HT . These properties are confirmed in the simulations. The second part of the thesis is concerned with robust estimation in panels of autoregressive time series. We investigate three different approaches. Firstly we robustify the above estimators in a direct way. Furthermore we generalise the robust autocovariance estimator of Ma and Genton (2000) to the panel case. We define a panel breakdown point for time series in two ways depending on the type of outliers assumed and compute its value for the panel autocovariance estimator. The estimated autocovariances are then used for the robust parameter estimation. Finally we propose an outlier test based upon the phase space representation of the time series in the panel, which can be used for eliminating outliers from the data set before using a non-robust method of estimation. We derive the asymptotic distribution of the test statistic and define a robust version of the test. For comparison we include other estimators in the analysis. The performance of the proposed robust procedures is investigated in a simulation study. For assessing the applicability of the above methods we analyse two sets of empirical data.