JOLrRNAL OF E nomet i ELSEVIER Journal of Econometrics 74 11996) 59-75 Testing the adequacy of smooth transition autoregressive models Oyvind Eitrheima, Timo Ter/isvirta*'a'b aResearch Department, Norges Bank (Central Bank of Norway), N-OI07 Oslo, Norway bDepartment of'Economic Statistics, Stockholm School of Economics, S-113 83 Stockholm, Sweden Abstract Smooth transition autoregressivc models are a flexible family of nonlinear time series models that have also been used for modelling economic data. This paper contributes to the evaluation stage of a proposed specification, estimation, and evaluation cycle of these models by introducing a Lagrangemultiplier (LM) test for the hypothesis of no error autocorrelation and LM-type tests for the hypothesis of no remaining nonlinearity and that of parameter constancy. Small-sample properties of the F versions of these tests and some alternative test statistics are investigated by simulation. The results indicate that the proposed tests can be applied in small samples already. Key words: STAR models; Parameter constancy; Nonlinear time series; Residual nonlin- earity test J E L classification: C22; C52 *Corresponding author. A part of the work for this paper was done while the second author was visiting the Institute of Theoretical Statistics, Copenhagen Business School. He is grateful to the Danish Social Science Research Council and the Danish Research Academy for financial support. Earlier versions of the paper were presented at the Econometric Society European Meeting, Uppsala, August 1993, the International Conference on Asymmetries and Nonlinearities in Dynamic Econometric Models, Madrid, January 1994, the Workshop on Non-Linear Modelling in Economics, Arhus, November 1994, the Workshop on Non-Linear Dynamic Phenomena in Economic and Financial Markets, Sydney, December 1994, and a seminar at the Christian-Albrechts-Universit~it Kiel. We wish to thank participants at these meetings and workshops for their comments, Hans-Jergen Bakk¢ and Dag Tjostheim for helpful discussions, a referee for insightful comments, and Vidar HjeUvik for allowing us to use his software for carrying out the nonparametric tests. The responsibility for any errors and shortcomings remain ours. 0304-4076/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSDI 0304-4076195)01 751-X