×

On limit theorems for functional autoregressive processes with random coefficients. (English) Zbl 07853857

MSC:

62Mxx Inference from stochastic processes
60Gxx Stochastic processes
60Fxx Limit theorems in probability theory

References:

[1] Nicholls, D.; Quinn, B., Random Coefficient Autoregressive Models: An Introduction, 1982, New York: Springer, New York · Zbl 0497.62081 · doi:10.1007/978-1-4684-6273-9
[2] Tjøsteim, D., Nonlinear time series: A selective review, Scand. J. Stat., 21, 97-130, 1994 · Zbl 0799.62098
[3] Tong, H., Nonlinear Time Series: A Dynamical System Approach, 1993, Oxford: Oxford Univ. Press, Oxford
[4] Bosq, D., Linear Process in Function Spaces: Theory and Applications, 2000, New York: Springer, New York · Zbl 0962.60004 · doi:10.1007/978-1-4612-1154-9
[5] Allam, A.; Mourid, T., Covariance operator estimation of a functional autoregressive process with random coefficients, Stat. Probab. Lett., 84, 1-8, 2014 · Zbl 1284.62541 · doi:10.1016/j.spl.2013.09.018
[6] Allam, A.; Mourid, T., Optimal rate for covariance operator estimators of functional autoregressive process with random coefficients, J. Multivariate Anal., 169, 130-137, 2019 · Zbl 1411.62135 · doi:10.1016/j.jmva.2018.07.009
[7] Boukhiar, S.; Mourid, T., Limit theorems for Hilbertian autoregressive processes with random coeffifients, Pub. Inst. Stat. Univ. Paris, 62, 59-74, 2018
[8] J. Cugliari, ‘‘Conditional autoregressive Hilbertian processes,’’ arXiv: 1302.3488 (2013).
[9] Guillas, S., Double stochastic Hilbertian processes, J. Appl. Probab., 39, 566-580, 2002 · Zbl 1017.60040 · doi:10.1239/jap/1034082128
[10] Mourid, T., Processus autoregressifs hilbertians a coefficients aleatoires, Ann. ISUP, 48, 79-86, 2004 · Zbl 1065.62158
[11] Gordin, M. I., The central limit theorem for stationary processes, Dokl. Akad. Nauk SSSR, 188, 739-741, 1969 · Zbl 0212.50005
[12] F. Merlevéde, M. Peligrad, and S. Utev, Functional Gaussian Approximation for Dependent Structures, Vol. 6 of Oxford Studies in Probability (Oxford Univ. Press, New York, 2019). · Zbl 1447.60003
[13] Dedecker, J.; Merlevéde, F., Necessary and sufficient conditions for the conditional central limit theorem, Ann. Probab., 30, 1044-1081, 2002 · doi:10.1214/aop/1029867121
[14] Dedecker, J.; Merlevéde, F., Convergence rates in the law of large numbers for Banach-valued dependent variables, Teor. Veroyatn. Primen., 52, 562-587, 2007 · Zbl 1158.60009 · doi:10.4213/tvp78
[15] Merlevéde, F., On the central limit theorem and its weak invariance principle for strongly mixing sequences with values in a Hilbert space via martingale approximation, J. Theor. Probab., 16, 625-653, 2003 · Zbl 1038.60029 · doi:10.1023/A:1025668415566
[16] Lesigne, E.; Volný, D., Large derivations for martingales, Stoch. Process. Appl., 96, 143-159, 2001 · Zbl 1059.60033 · doi:10.1016/S0304-4149(01)00112-0
[17] Pisier, G., Martingales with values in uniformly convex spaces, Israel J. Math., 20, 326-350, 1975 · Zbl 0344.46030 · doi:10.1007/BF02760337
[18] P. Assouad, ‘‘Espaces \(p\)-lisses et \(q\)-convexes, inégalités de Bukrholder,’’ in Proceedings of the Séminaire Maurey-Schwartz 1974-1975: Espaces \(L^p\), applications radionifiantes et géométrie des espaces Banach (1975), p. 15. · Zbl 0318.46023
[19] Andel, J., Autoregressive series with random parameters, Math. Operationsf. Stat., 7, 735-741, 1976 · Zbl 0346.62066 · doi:10.1080/02331887608801334
[20] Aue, A.; Horvath, L.; Steinebach, J., Estimation in random coefficient autoregressive models, J. Time Ser. Anal., 27, 61-76, 2006 · Zbl 1112.62084 · doi:10.1111/j.1467-9892.2005.00453.x
[21] Bougerol, P.; Picard, N., Strict stationarity of generalized autoregressive processes, Ann. Probab., 20, 1714-1730, 1992 · Zbl 0763.60015 · doi:10.1214/aop/1176989526
[22] Brandt, A., The stochastic equation \(Y_{n+1}=A_nY_n+B_n\), Adv. Appl. Probab., 18, 211-220, 1986 · Zbl 0588.60056
[23] Mourier, E., “Éléments aleatoires dans un espace de Banach,” Ann. Inst. H, Poincaré, 13, 161-244, 1953 · Zbl 0053.09503
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.