Abstract
In earlier chapters the restrictions of ∣ϱ∣ < 1/λ p for the conditional model and ∣ϱ∣ < 1 for the simultaneous model employing matrix W (the stochastic version of matrix C) were employed to insure stationarity [i.e., (I - ϱC)-1 and (I - ϱW)-1 will be convergent series in their geometric series expansion forms], as well as invertibility between the autoregressive and moving average models. The restrictions also are necessary for writing the spectral density counterparts of spatial autoregressive models. The aim of this chapter is to outline spectral representations of spatial auto- regressive models for both infinite and finite regular tessellation surfaces. In doing so, the selected tabular results presented in Bartlett (1975) will be extended. A second use of spectral analysis to be studied here has to do with the quantitative analysis of two-dimensional shapes. The dual axis Fourier analysis approach to constructing shape indices will be reviewed and evaluated.
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© 1988 Kluwer Academic Publishers, Dordrecht
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Griffith, D.A. (1988). Spatial Autocorrelation and Spectral Analysis. In: Advanced Spatial Statistics. Advanced Studies in Theoretical and Applied Econometrics, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2758-2_5
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DOI: https://doi.org/10.1007/978-94-009-2758-2_5
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