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Biometrika 1987 74(1):103-113; doi:10.1093/biomet/74.1.103
© 1987 by Biometrika Trust
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Contemporaneous bivariate time series

F. CAMACHO, A. I. MCLEOD and K. W. HIPEL

Department of Statistical and Actuarial Sciences, University of Western Ontario London, Ontario, Canada N6A 5B9
Department of Systems Design Engineering, University of Waterloo Waterloo, Ontario, Canada N2L 3G1

Bivariate autoregressive-moving average time series with diagonal parameter matrices for the autoregressive and moving average components exhibit only contemporaneous or instantaneous correlation. In practice, different lengths of each series may be available. An efficient maximum likelihood algorithm for parameter estimation is derived. The statistical efficiency of this new procedure is compared with that of the standard multivariate and univariate procedures which utilize only part of the available data.

Key Words: Autoregressive-moving average model • Contemporaneous Granger causality • Multiple time series • Statistical efficiency


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