摘要:

We define time series in m dimensions x, as follows: the observed variable z depends on and similarly n time series in m variables where f(x,t) and x are vectors. This is the discrete case. The continuous case is similar. Distinction is made between m time series in zero dimension, at a particular point x, and one time series in m dimensions.

ISSN:0361-0918    

DOI:10.1080/03610918008812168

出版商:Marcel Dekker, Inc.    

年代:1980

数据来源: Taylor

摘要:

Stochastic models for discrete time series in the time domain are well known but such models lack consideration of spatial dependency I We expand on their work by constructing spatially dependent moving average models. Definitions of order, stationarity, invertibility, autocorrelation function, and spectrum are made as natural extensions of those in zero dimensions and are implemented in the one and two-space dimensional models.

ISSN:0361-0918    

DOI:10.1080/03610918008812169

出版商:Marcel Dekker, Inc.    

年代:1980

数据来源: Taylor

摘要:

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

ISSN:0361-0918    

DOI:10.1080/03610918008812170

出版商:Marcel Dekker, Inc.    

年代:1980

数据来源: Taylor

摘要:

The paper describes a general linear stochastic model which supposes a time series to be generated by a linear aggregation of random shocks at various temporal and spatial locations. It is a combination of autoregressive and moving average models (ARMA). The autocorrelation functions and power spectra are determined,

ISSN:0361-0918    

DOI:10.1080/03610918008812171

出版商:Marcel Dekker, Inc.    

年代:1980

数据来源: Taylor

摘要:

The mechanics of the procedure for building space-time autoregressive moving average (STARMA) models is dependent upon the form of G, the variance-covariance matrix of the underlying errors.This paper presents large sample tests of the hypotheses that G is diagonal and that G equals o2I. Tables of the critical values for these tests are constructed

ISSN:0361-0918    

DOI:10.1080/03610918008812172

出版商:Marcel Dekker, Inc.    

年代:1980

数据来源: Taylor

摘要:

The building of STARMA, space-time autoregressive moving average, models requires a working knowledge of the conditions under which a particular model represents a stationary process. Constraints on the parameter space that ensure stationarity are developed for all STARMA models of autoregressive temporal order le*ss than or equal to two and spatial order less than or equalto one when the model form utilizes scaled weights. Invertibility conditions for these same models are also given.

ISSN:0361-0918    

DOI:10.1080/03610918008812173

出版商:Marcel Dekker, Inc.    

年代:1980

数据来源: Taylor

ISSN:0361-0918    

DOI:10.1080/03610918008812167

出版商:Marcel Dekker, Inc    

年代:1980

数据来源: Taylor