A non-parametric test for generalized first-order autoregressive models

Scandinavian Journal of Statistics

Volumn 24, Issue 2, 1997, Pages 241-259

  Diebolt, Jean ^a   Wandji, Joseph Ngatchou ^b  

^a LMC   (France)

^b UNIVERSITÉ PARIS 13   (France)

Author keywords

Autoregressive models; Functional limiting distribution; Goodness of fit tests; Mixing; Non linear models; Non parametric methods; Weak invariance principle

Indexed keywords

EID: 0041108451     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00061     Document Type: Article

References (24)

1. Benghabrit, Y. & Hallin, M. (1996). Locally asymptotically optimal test for autoregressive against bilinear serial dependence. Statistica Sinica 6, 147-170.
2. Billingsley, P. (1968). Convergence of probability measures. Wiley, New York.
3. Chen, R., Liu, J. S. & Tsay, R. S. (1995). Additivity test for nonlinear autoregression. Biometrika 82, 368-383.
4. Diebolt, J. (1990). Testing the function defining a nonlinear autoregressive time series. Stochastic Process. Appl. 36, 85-106.
5. Diebolt, J. & Ngatchou Wandji, J. (1995). Un test non-paramétrique pour un modèle bilinéaire diagonal d'ordre un. C. R. Acad. Sci. Paris Ser. I 320, 1135-1139.
6. Doukhan, P. (1994). Mixing: properties and examples. Lecture Notes in Statistics, 85, Springer, New York.
7. Doukhan, P. & Portal, F. (1987). Principe d'invariance faible pour la fonction de répartition empirique dans un cadre multidimensionnel et fortement mélangeant. Probab. Math. Statist. 8, 117-132.
8. Doukhan, P., Leon, J. & Portal, F. (1985). Calcul de la vitesse de convergence dans le théorème central limite vis-à-vis des distances de Prohorov, Dudley et Lévy dans le cas des variables aléatoires dépendantes. Probab. Math. Statist. 6, 19-27.
9. Dudley, R. & Phillip, W. (1983). Invariance principles for sums of Banach space valued random variables. Z. Wahrsch. verw. Gebiete 63, 393-432.
10. Guégan, D. & Ngatchou Wandji, J. (1996). Power of the Lagrange multiplier test for certain subdiagonal bilinear models. Statist. Probab. Lett. 29, 201-212.
11. Grill, K. (1991). A lim inf result in Strassen's law of the iterated logarithm. Probab. Theory Related Fields 89, 149-157.
12. Hjellvik, V. & Tjøstheim, D. (1995). Nonparametric tests of linearity for time series. Biometrika 82, 355-368.
13. Hili, O. (1995). On the estimation of nonlinear time series models. Stochast. Stochast. Rep. 52, 207-226.
14. Luukkonen, R., Saikkonnen, P. & Terasvirta, T. (1988). Testing linearity in univariate time series models. Scand. J. Statist. 15, 167-175.
15. Mokkadem, A. (1990). Propriétés de mélange de processus autoregressifs polynomiaux Ann. Inst. Henri Poincaré Probab. Statist. 26, 219-260.
16. Ngatchou Wandji, J. (1995). Étude de tests paramétriques et non-paramétriques asymptotiquement puissants pour les modéles autorégressifs bilinéaires. Thèse, Université Paris 13.
17. Ozaki, T. (1980). Nonlinear time series models for nonlinear random vibrations. J. Appl. Probab. 17, 84-93.
18. Pham, T. D. & Tran, L. T. (1981). On the first order bilinear time series models. J. Appl. Probab. 18, 617-627.
19. Poggi, J. M. & Portier, B. (1995). Un test de linéarité pour les modèles autorégressifs fonctionnels. C. R. Acad. Sci. Paris Ser. I 321, 113-116.
20. Saikkonen, P. & Luukkonen, R. (1988). Lagrange multiplier tests for testing non linearites in time series models. Scand. J. Statist. 15, 55-68.
21. Shorack, G. & Wellner, J. (1986). Empirical processes with applications to statistics. Wiley, New York.
22. Strassen, V. (1965). The existence of probability measures with given marginals. Ann. Math. Statist. 36, 423-439.
23. Tjøstheim, D. & Skaug, H. (1993). A nonparametric test of serial independence based on the empirical distribution function. Biometrika 80, 591-602.
24. Tong, H. (1990). Nonlinear time series. Clarendon Press, Oxford.