摘要:

Abstract.The problem of estimating the order of autoregressive models is considered from the point of view of ranking and selection procedures. This approach offers a formulation to many problems more realistic than that of classical hypothesis testing or of criteria based on estimation theory (e.g., AIC). In the method considered here, sampling variations are taken into account and the experimenter is also allowed to incorporate any a priori knowledge of the true order (e.g., lower bound as well as upper bound).

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1984.tb00383.x

出版商:Blackwell Publishing Ltd    

年代:1984

数据来源: WILEY

摘要:

Abstract.Conditions under which sums, products and time‐aggregation of ARMA processes follow ARMA models are derived from a single theorem. This characterizes these processes in terms of difference equations satisfied by their autocovariance function. From this we obtain necessary and sufficient conditions for a function of a Gaussian ARMA process and the product of two possibly dependent Gaussian ARMA processes to be ARMA. We show that the sum and product of two ARMA processes related by a Box and Jenkins transfer function model belong to the ARMA famil

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1984.tb00384.x

出版商:Blackwell Publishing Ltd    

年代:1984

数据来源: WILEY

摘要:

Abstract.For the bilinear time seriesXt=βXt‐ket‐l+ev,k≥l, formulas for the firstk‐1 autocorrelations ofX2tare obtained. These results fill in a gap in Granger and Andersen (1978). Simulation experiments are used to study the applicability of theoretical results and to investigate some more general situations. It is found that if ß is not too small,kandlmay be identified using the autocorrelations ofX2t. Application to more general situations is also briefly

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1984.tb00385.x

出版商:Blackwell Publishing Ltd    

年代:1984

数据来源: WILEY

摘要:

Abstract.This paper reviews several different methods for identifying the orders of autoregressive‐moving average models for time series data. The case is made that these have a common basis, and that a unified approach may be found in the analysis of a matrix G, defined to be the covariance matrix of forecast values.The estimation of this matrix is considered, emphasis being placed on the use of high order autoregression to approximate the predictor coefficients. Statistical procedures are proposed for analysing G, and identifying the model orders.A simulation example and three sets of real data are used to illustrate the procedure, which appears to be a very useful tool for order identification and preliminary model estimatio

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1984.tb00386.x

出版商:Blackwell Publishing Ltd    

年代:1984

数据来源: WILEY