Time series in m dimensions: Autoregressive models
- 1 January 1980
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Simulation and Computation
- Vol. 9 (5) , 491-513
- https://doi.org/10.1080/03610918008812170
Abstract
Spatially dependent autoregressive models in m dimensions are defined. The conditions for stationarity and invertibility are determined. The autocorrelation function and Yule-Walker equations are obtained for the general case, and as particular cases for special discrete values for various grids in plane and for orders 1 and 2 in time. The spectra are obtained for these particular cases, and some results for the partial autocorrelation function. All results are new. The notation, definitions, and assumptions are those given by Voss et al. (1980). We assume stationarity of z over time t, where an m dimensional vec 12m tor. We assume the covariance structure as given by Hannan (1970), 2 with and all covariances existing. Nonstationary models will be considered in later papers.Keywords
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