caa a22 4500 386371822 CHVBK 20180307112000.0 cr unu---uuuuu 161130e198904 xx s 000 0 eng 10.1017/S026646660001224X doi S026646660001224X pii (NATIONALLICENCE)cambridge-10.1017/S026646660001224X Mirror-Image and Invariant Distributions in ARMA Models [Elektronische Daten] The finite sample distributions of estimators and test statistics in ARMA time series models are generally unknown. For typical sample sizes, the approximations provided by asymptotic distributions are often unsatisfactory. Hence simulation or numerical integration methods are used to investigate the distributions. In practice only a limited part of the parameter space is examined using these methods. Thus any results which allow us to infer properties from one portion of the parameter space to another or to establish symmetry are most welcome. For the ARMA model estimated with no intercept term, we show that the least-squares and maximum likelihood estimators have mirror-image invariant or symmetric distributions. The F, t, likelihood ratio, Wald, and Lagrange multiplier statistics are also shown to have distributions with certain mirror-image invariant or symmetry properties. The analysis is extended to misspecified models as well as to ARMA spectral densities. These properties would have been helpful in either simplifying or extending much earlier work in this area. Copyright © Cambridge University Press 1989 Cryer Jonathan D. University of Iowa Nankervis John C. City of London Polytechnic Savin N.E. University of Iowa Econometric Theory Cambridge University Press 5/1(1989-04), 36-52 0266-4666 5:1<36 1989 5 ECT https://doi.org/10.1017/S026646660001224X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S026646660001224X text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cryer Jonathan D. University of Iowa NATIONALLICENCE 700 1- Nankervis John C. City of London Polytechnic NATIONALLICENCE 700 1- Savin N.E. University of Iowa NATIONALLICENCE 773 0- Econometric Theory Cambridge University Press 5/1(1989-04), 36-52 0266-4666 5:1<36 1989 5 ECT CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge