A mixed-type test for linearity in time series

Journal of Statistical Planning and Inference

Volumn 88, Issue 2, 2000, Pages 339-353

  An, Hong Zhi ^a   Zhu, Li Xing ^a   Li, Run Ze ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

62G10; 62H15; Nonlinearity; Primary 62M10; Secondary 62E10; Stationary AR( p ) series; Test for linearity

Indexed keywords

EID: 0042284737     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(00)00087-2     Document Type: Article

References (23)

1. An H.Z., Chen Z.G., Hannan E.J. Autocorrelation, autoregression and autoregressive approximation. Ann. Statist. 10:1982;926-936.
2. An H.Z., Cheng B. A Kolmogorov-Smirnov type statistic with application to test for nonlinearity in time series. Int. Statist. Rev. 59:1991;287-307.
3. Ashley R.A., Patherson D.M., Hinich M.J. A diagnostic test for nonlinearity serial dependence in time series fitting errors. J. Time Ser. Anal. 7:1986;165-178.
4. Box G.E.P., Jenkins G.M. Time Series Analysis: Forecasting and Control. 1970;Holden-Day, San Francisco.
5. Brockett P.L., Hinich M., Wilson G.R. Nonlinear and non-Gaussianocean noise. J. Amer. Statist. Assoc. 82:1987;1386-1394.
6. Chan W.S., Tong H. On test for nonlinearity in time series analysis. J. Forecasting. 5:1986;217-228.
7. Chen, X.R., Krishnaiah, P.R., 1990. A test of linearity of regression models. Chinese J. Appl. Probab. Statist. 6, 363-377 (in Chinese).
8. Chow Y.S., Teicher H. Probability Theory. 1978;Springer, New York.
9. Cox D.D., Koh E. A smoothing spline based test of model adequacy in polynomial regression. Ann. Inst. Statist. Math. 41:1989;383-400.
10. Eubank R.L., Spiegelman C.H. Testing the goodness of fit of a linear model via nonparametric regression techniques. J. Amer. Statist. Assoc. 85:1990;387-392.
11. Hall P., Heyde C.C. Martingale Limit Theory and its Application. 1980;Academia Press, New York.
12. Hinich M. Testing for Gaussianity and linearity of a stationary time series. J. Time Ser. Anal. 3:1982;169-176.
13. Hjellivik, V., Tj φ stheim, D., 1993. Nonparametric tests of linearity for time series. Biometrika.
14. Keenan P.J. A turkey nonadditivity-type test for time series. Biometrika. 72:1985;39-44.
15. Loeve M. Probability Theory. 2nd Edition. 1960;Van Nostrand Reinhold, New York.
16. Luukkonen R., Saikkonen P., Terasvirta T. Testing linearity against smooth transition autoregression. Biometrika. 75:1988;491-499.
17. Saikkonen P., Luukkonen R. Lagrange multiplier test for testing nonlinearity in time series models. Scand. J. Statist. 15:1988;55-68.
18. Subba Rao T., Gabr M.M. A test for linearity of stationary time series. J. Time Ser. Anal. 1:1980;145-158.
19. Terästirta, Tet al. Power of the neural network linearity test. J. Time Ser. Anal. 14:1993;209-220.
20. Tong H. Non-linear Time Series. 1990;Oxford University Press, Oxford, New York.
21. Tsay R. Nonlinearity tests for time series. Biometrika. 73:1986;237-252.
22. Zhu, L.X., An, H.Z., 1992. A testing approach for nonlinearity in regression models. J. Math. 4, 391-397 (in Chinese).
23. Zhu L.X., Hichernell F., An H.Z. A goodness of fit test for linearity of a stochastic regression model. Chinese J. Comtemp. 36:1993;199-206.