Adaptive test for periodicity in restrictive EXPAR(p) models

References

• Allal, J., and S. El Melhaoui. 2006. Optimal detection of exponential component. Journal of Time Series Analysis 27 (6):793–810. doi:10.1111/j.1467-9892.2006.00489.x.
   Web of Science ®Google Scholar
• Azouagh, N., and S. El Melhaoui. 2019. An exponential autoregressive model for the forecasting of annual sunspots number. Electronic Journal of Mathematical Analysis and Applications 7 (3):17–23.
   Google Scholar
• Baragona, R., F. Battaglia, and D. Cuccina. 2002. A note on estimating autoregressive exponential models. Quaderni di Statistica 4:1–18.
   Google Scholar
• Bentarzi, M., H. Guerbyenne, and M. Merzougui. 2009. Adaptive test for periodicity in self-exciting threshold autoregressive models. Communications in Statistics - Simulation and Computation 38 (8):1592–609. doi:10.1080/03610910903061006.
   Web of Science ®Google Scholar
• Bentarzi, M., and M. Hallin. 1996. Locally optimal tests against periodic autoregression. Econometric Theory 12 (1):88–112. doi:10.1017/S0266466600006459.
   Web of Science ®Google Scholar
• Bentarzi, M., and M. Merzougui. 2010. Adaptive test for periodicity in autoregressive conditional heteroskedastic processes. Communications in Statistics - Simulation and Computation 39 (9):1735–53. doi:10.1080/03610918.2010.512694.
   Web of Science ®Google Scholar
• Bibi, A., and A. Gautier. 2005. Stationarity and asymptotic inference of some periodic bilinear models. Comptes Rendus Mathematique 341 (11):679–82. doi:10.1016/j.crma.2005.09.040.
   Web of Science ®Google Scholar
• Bickel, P. J. 1982. On adaptive estimation. The Annals of Statistics 10 (3):647–71. doi:10.1214/aos/1176345863.
   Web of Science ®Google Scholar
• Bollerslev, T., and E. Ghysels. 1996. Periodic autoregressive conditional heteroskedasticity. Journal of Business and Economic Statistics 14:139–52.
   Web of Science ®Google Scholar
• Chan, K. S., and H. Tong. 1985. On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations. Advances in Applied Probability 17 (3):666–78. doi:10.2307/1427125.
   Web of Science ®Google Scholar
• De Gooijer, J. G. 2017. Elements of nonlinear time series analysis and forecasting. New York, NY: Springer International Publishing.
   Google Scholar
• Franses, P. H., and M. Ooms. 1997. A periodic long memory model for quarterly UK inflation. International Journal of Forecasting 13 (1):117–28. doi:10.1016/S0169-2070(96)00715-7.
   Web of Science ®Google Scholar
• Ghosh, H., B. Gurung, and P. Gupta. 2015. Fitting EXPAR models through the extended Kalman filter. Sankhyā: The Indian Journal of Statistics 77 (1):27–44.
   Google Scholar
• Gladyshev, E. G. 1961. Periodically correlated random sequences. Soviet Mathematics 2:385–8.
   Google Scholar
• Haggan, V., and T. Ozaki. 1981. Modeling nonlinear random vibrations using an amplitude-dependent autoregressive time series model. Biometrika 68 (1):189. doi:10.1093/biomet/68.1.189.
   Web of Science ®Google Scholar
• Hájek, J., and Z. Šidák. 1967. Theory of rank tests. New York, NY: Academic Press.
   Google Scholar
• Hallin, M., and S. Lot Fi. 2004. Optimal detection of periodicities in vector autoregressive models. In Statistical modeling and analysis for complex data problems, 49–75. Boston, MA: Springer.
   Google Scholar
• Kreiss, J. P. 1987. On adaptive estimation in stationary ARMA processes. The Annals of Statistics 15 (1):112–33. doi:10.1214/aos/1176350256.
   Web of Science ®Google Scholar
• Le Cam, L. 1986. Asymptotic methods in statistical decision theory. New York, NY: Springer-Verlag.
   Google Scholar
• Le Cam, L. 1960. Locally asymptotically normal families of distributions. University of California Publications in Statistics 3:37–98.
   Google Scholar
• Merzougui, M., and S. Becila. 2019. Least squares estimation in periodic restricted EXPAR(p) Models. International Journal of Statistics: Advances in Theory and Applications 1 (2):275–91.
   Google Scholar
• Merzougui, M., H. Dridi, and A. Chadli. 2016. Test for periodicity in restrictive EXPAR models. Communication in Statistics - Theory and Methods 45 (9):2770–83. doi:10.1080/03610926.2014.887110.
   Web of Science ®Google Scholar
• Ozaki, T. 1980. Non-linear time series models for non-linear random vibrations. Journal of Applied Probability 17 (1):84–93. doi:10.2307/3212926.
   Web of Science ®Google Scholar
• Ozaki, T. 1982. The statistical analysis of perturbed limit cycle processes using nonlinear time series models. Journal of Time Series Analysis 3 (1):29–41. doi:10.1111/j.1467-9892.1982.tb00328.x.
   Google Scholar
• Ozaki, T. 1985. Non linear time series models and dynamical system. Handbook of Statistics 5:25–83.
   Google Scholar
• Swensen, A. R. 1985. The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend. Journal of Multivariate Analysis 16 (1):54–70. doi:10.1016/0047-259X(85)90051-X.
   Web of Science ®Google Scholar