TY - JOUR
T1 - On the nature of SEM estimates of ARMA Parameters
AU - Hamaker, Ellen L.
AU - Dolan, Conor V.
AU - Molenaar, Peter C.M.
N1 - Funding Information:
The research of Conor Dolan has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. We thank Michael W. Browne for his helpful suggestions.
Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2002
Y1 - 2002
N2 - Several papers have been devoted to the use of structural equation modeling (SEM) software in fitting autoregressive moving average (ARMA) models to a univariate series observed in a single subject. Van Buuren (1997) went beyond specification and examined the nature of the estimates obtained with SEM software. Although the results were mixed, he concluded that these parameter estimates resemble true maximum likelihood (ML) estimates. Molenaar (1999) argued that the negative findings for pure moving average models might be due to the absence of invertibility constraints in Van Buuren's simulation experiment. The aim of this article is to (a) reexamine the nature of SEM estimates of ARMA parameters; (b) replicate Van Buuren's simulation experiment in light of Molenaar's comment; and (c) examine the behavior of the log-likelihood ratio test.We conclude that estimates of ARMA parameters obtained with SEM software are identical to those obtained by univariate stochastic model preliminary estimation, and are not true ML estimates. Still, these estimates, which may be viewed as moment estimates, have the same asymptotic properties as ML estimates for pure autoregressive (AR) processes. For pure moving average (MA) processes, they are biased and less efficient. The estimates from SEM software for mixed processes seem to have the same asymptotic properties as ML estimates. Furthermore, the log-likelihood ratio is reliable for pure AR processes, but this is not the case for pure MA processes. For mixed processes, the behavior of the log-likelihood ratio varies, and in this case these statistics should be handled with caution.
AB - Several papers have been devoted to the use of structural equation modeling (SEM) software in fitting autoregressive moving average (ARMA) models to a univariate series observed in a single subject. Van Buuren (1997) went beyond specification and examined the nature of the estimates obtained with SEM software. Although the results were mixed, he concluded that these parameter estimates resemble true maximum likelihood (ML) estimates. Molenaar (1999) argued that the negative findings for pure moving average models might be due to the absence of invertibility constraints in Van Buuren's simulation experiment. The aim of this article is to (a) reexamine the nature of SEM estimates of ARMA parameters; (b) replicate Van Buuren's simulation experiment in light of Molenaar's comment; and (c) examine the behavior of the log-likelihood ratio test.We conclude that estimates of ARMA parameters obtained with SEM software are identical to those obtained by univariate stochastic model preliminary estimation, and are not true ML estimates. Still, these estimates, which may be viewed as moment estimates, have the same asymptotic properties as ML estimates for pure autoregressive (AR) processes. For pure moving average (MA) processes, they are biased and less efficient. The estimates from SEM software for mixed processes seem to have the same asymptotic properties as ML estimates. Furthermore, the log-likelihood ratio is reliable for pure AR processes, but this is not the case for pure MA processes. For mixed processes, the behavior of the log-likelihood ratio varies, and in this case these statistics should be handled with caution.
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U2 - 10.1207/S15328007SEM0903_3
DO - 10.1207/S15328007SEM0903_3
M3 - Article
AN - SCOPUS:18444364748
SN - 1070-5511
VL - 9
SP - 347
EP - 368
JO - Structural Equation Modeling
JF - Structural Equation Modeling
IS - 3
ER -