Abstract
A special class of linear stationary spatial time series models: Space-Time ARMA(STARMA) models, has been proven useful in modelling observations measured in space and time. A review of STARMA models and modelling procedure is presented. An order determination method and approach for initial estimation of the model parameters are proposed. The STARMA modelling procedure and extensions are implemented and tested using simulated data. Then the Performance in forecasting of the STARMA model is compared with that of separate univariate ARMA models. This comparison is performed using real data of monthly mean temperatures from nine meteorological stations around the United Kingdom.
Article Note
The work of the author was supported by FCT Grant SFRH/BD/1473/2000 (Fundacao para a Ciencia e a Tecnologia, Portugal) and the author is Grateful for the grant.
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References
Akaike H., Time Series analysis and control through parametric models, in Applied Time Series Analysis, D.F. Findley (ed.) Academic Press. New York, 1978.
Chatfield C., Time Series Forecasting, Boca Raton, Chapman and Hall/CRC, 2001.
D’Agostino R.B., Stevens M A. eds, Goodness-of-fit techniques, Marcel Dekker, 1986.
Deutsch S.J. and Pfeifer P.E., Space-time ARMA modelling with contemporaneously correlated innovations, Technometrics (1981), 23, 401–9.
Hannan E.J. and Rissanen J., Recursive estimation of mixed autoregressive-moving average order, Biometrika (1982), 69(1), 81–94.
Haslett J. and Raftery A.E., Space-time Modelling with Long-memory Dependence: Assessing Ireland’s Wind Power Resource, Appl. Statist. (1989), 38, 1–50.
Marquardt D.W., An Algorithm for least squares estimation of non-linear parameters, Jour. Soc. Ind. Appl. Math. (1963), 11, p. 413.
Pfeifer P.E. and Deutsch S.J., A three stage interactive procedure for space-time modeling, Technometrics (1980a), 22, 35–47.
Pfeifer P.E. and Deutsch S.J., Identification and interpretation of first order space-time ARMA models, Technometrics (1980b), 22, 397–408.
Pfeifer P.E. and Deutsch S. J., Independence and sphericity tests for the residuals of space-time ARIMA Models, Communications in Statistics. B — Simulation and Computation (1980d), 9 (5), 533–549.
Pfeifer P.E. and Deutsch S.J., Seasonal space-time modelling, Geographical Analysis (1981a), 13, 117–33.
Pfeifer P.E. and Deutsch S.J., Variance of the sample space-time Autocorrelation Function, J. Roy. Statist. Soc. Ser. B (1981b), 43(1), 28–33.
Pfeifer P.E. and Bodily S.E., A test of Space-time ARMA Modelling and Forecasting of Hotel data, J. Forecasting (1990), 9, 255–272.
Smith R.L., Spatial Statistics in Environmental Science. In Nonlinear and Nonstationary Signal Processing, W.J. Fitzgerald, R.L. Smith, A. Warden, and P.C. Young, eds, 2000.
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© 2004 Springer-Verlag New York,LLC
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Subba Rao, T., Costa Antunes, A.M. (2004). Spatio-temporal Modelling of Temperature Time Series: A Comparative Study. In: Brillinger, D.R., Robinson, E.A., Schoenberg, F.P. (eds) Time Series Analysis and Applications to Geophysical Systems. The IMA Volumes in Mathematics and its Applications, vol 45. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2962-9_7
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DOI: https://doi.org/10.1007/978-1-4612-2962-9_7
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