Optimal Tests for Distinguishing PAR Models from PSETAR Models
Keywords:
Periodic Self-Exciting Threshold Autoregressive, Local Asymptotic Normality, Local Asymptotic optimal test, Kernel estimation.
Abstract
This paper aims to detect nonlinearity in periodic autoregressive models. We introduce parametric and semiparametric local asymptotic optimal tests designed for distinguishing a periodic autoregressive model from a periodic self-exciting threshold autoregressive (SETAR) model. Leveraging the Local Asymptotic Normality (LAN) property specific to periodic SETAR models, we devise a parametric test that is locally asymptotically most stringent. Additionally, the utilization of kernel estimation for the density function allows the construction of an adaptive test for enhanced flexibility and accuracy in detecting nonlinearity.References
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(12) Merzougui, M. (2016). Optimal Test for PAR(1) dependence against PSETAR(2,1,1) Models with specified Threshold. Communications in Statistics - Theory and Methods, 45(4), 872-886.
(13) Shao, Q. (2006). Mixture periodic autoregressive time series model. Statistics & Probability Letters, 76(6), 609-618.
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(15) Tong, H. (1978). On threshold models. In Pattern Recognition and Signal Processing, (Ed. C. H. Chen). Amsterdam: Sijhoff & Noordhoff.[vskip]\vskip 3mm
(2) Aknouche, A. & Guerbyenne, H. (2009a). On some probabilistic properties of double periodic AR models. Statistics & Probability Letters, 79, 407-413.
(3) Bentarzi, M., & Djeddou, L. (2014). Adaptive Estimation of Periodic First-Order Threshold Autoregressive Model. Communications in Statistics - Simulation and Computation, 43(7), 1611-1630.
(4) Bibi, A., & Gautier, A. (2005). Stationarity and asymptotic inference of some periodic bilinear models. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 341(9), 679-682.(2).
(5) Bollerslev, T., & Ghysels, E. (1996). Periodic Autoregressive Conditional Heteroskedasticity. Journal of Business and Economic Statistics, 14(2), 139-152.
(6) Gladyshev, E. G. (1961). Periodically correlated random sequences. Soviet Mathematics, 2, 385-388.
(7) Hájek, J., & Šidák, Z. (1967). Theory of Rank Tests. Academic Press, New York.[vskip]
(8) Kreiss, J. P. (1987). On Adaptive Estimation in Stationary ARMA Processes. The Annals of Statistics, 15(1), 112-133.[vskip]
(9) Le Cam, L. (1986). Asymptotic Methods in Statistical Decision Theory. Springer-Verlag, New York.[vskip]
(10) Le Cam, L. (1960). Locally Asymptotically Normal Families of Distributions. University of California Publications in Statistics, 3, 37-98.[vskip]
(11) Lewis, P. A. W., & Ray, B. K. (2002). Nonlinear modelling of periodic threshold autoregressions using TSMARS. Journal of Time Series Analysis, 23(4), 459-471.
(12) Merzougui, M. (2016). Optimal Test for PAR(1) dependence against PSETAR(2,1,1) Models with specified Threshold. Communications in Statistics - Theory and Methods, 45(4), 872-886.
(13) Shao, Q. (2006). Mixture periodic autoregressive time series model. Statistics & Probability Letters, 76(6), 609-618.
(14) Swensen, A. R. (1985). The Asymptotic Distribution of the likelihood ratio for autoregressive time series with a regression trend. Journal of Multivariate Analysis, 16, 54-70.[vskip]
(15) Tong, H. (1978). On threshold models. In Pattern Recognition and Signal Processing, (Ed. C. H. Chen). Amsterdam: Sijhoff & Noordhoff.[vskip]
Published
2025-02-06
How to Cite
Bezziche, N., & Merzougui, M. (2025). Optimal Tests for Distinguishing PAR Models from PSETAR Models. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2240
Issue
Section
Research Articles
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