Robust Inference for Nonstationary Time Series with Possibly Multiple Changing Periodic Structures

References

• Boente, G., He, X., and Zhou, J. (2006), “Robust Estimates in Generalized Partially Linear Models,” Annals of Statistics, 34, 2856–2878.
   Web of Science ®Google Scholar
• Bunea, F. (2004), “Consistent Covariate Selection and Post Model Selection Inference in Semiparametric Regression,” Annals of Statistics, 32, 898–927.
   Web of Science ®Google Scholar
• Cai, Z., Fan J., and Li R. (2000), “Efficient Estimation and Inferences for Varying Coefficient Models,” Journal of the American Statistical Association, 95, 888–902. DOI: 10.1080/01621459.2000.10474280.
   Web of Science ®Google Scholar
• Chen Y. C., Cheng M. Y., and Wu, H. T. (2014), “Nonparametric and Adaptive Modeling of Dynamical Periodicity and Trend With Heteroscedastic and Dependent Errors,” Journal of the Royal Statistical Society, Series B, 76, 651–682. DOI: 10.1111/rssb.12039.
   Google Scholar
• Dahlhaus R. (2012), “Locally Stationary Processes,” in Handbook of Statistics (vol. 30), Elsevier, pp. 351–413.
   Google Scholar
• De Boor, C. (1978), A Practical Guide to Splines (vol. 27). New York: Springer-Verlag.
   Google Scholar
• Fan J., and Zhang W. (1999), “Statistical Estimation in Varying-Coefficient Models,” Annals of Statistics, 27, 1491–1518.
   Web of Science ®Google Scholar
• Genton M. G., and Hall, P. (2007), “Statistical Inference for Evolving Periodic Functions,” Journal of the Royal Statistical Society, Series B, 69, 643–657. DOI: 10.1111/j.1467-9868.2007.00604.x.
   Google Scholar
• Hadj-Amar, B., Rand, B. F., Fiecas, M., Lev́i, F., and Huckstepp, R. (2020), “Bayesian Model Search for Nonstationary Periodic Time Series,” Journal of the American Statistical Association, 115, 1320–1335. DOI: 10.1080/01621459.2019.1623043.
   Web of Science ®Google Scholar
• Hall, P., Peng, L., and Yao, Q. (2002), “Prediction and Nonparametric Estimation for Time Series With Heavy Tails,” Journal of Time Series Analysis, 23, 313–331. DOI: 10.1111/1467-9892.00266.
   Web of Science ®Google Scholar
• Hall, P., Reimann, J., and Rice, J. (2000), “Nonparametric Estimation of a Periodic Function,” Biometrika, 87, 545–557. DOI: 10.1093/biomet/87.3.545.
   Web of Science ®Google Scholar
• Hall P., and Yin, J. (2003), “Nonparametric Methods for Deconvolving Multiperiodic Functions,” Journal of the Royal Statistical Society, Series B, 65, 869–886. DOI: 10.1046/j.1369-7412.2003.00420.x.
   Google Scholar
• He X., Fung W. K., and Zhu, Z. (2005), “Robust Estimation in Generalized Partial Linear Models for Clustered Data,” Journal of the American Statistical Association, 100, 1176–1184. DOI: 10.1198/016214505000000277.
   Web of Science ®Google Scholar
• Huang, J., and Yang, L. (2004), “Identification of Non-Linear Additive Autoregressive Models,” Journal of the Royal Statistical Society, Series B, 66, 463–477. DOI: 10.1111/j.1369-7412.2004.05500.x.
   Google Scholar
• Huber, P. J. (1973), “Robust Regression: Asymptotics, Conjectures and Monte Carlo,” Annals of Statistics, 1, 799–821.
   Web of Science ®Google Scholar
• Ke, Y., Li, J., and Zhang, W. (2016), “Structure Identification in Panel Data Analysis,” Annals of Statistics, 44, 1193–1233.
   Web of Science ®Google Scholar
• Li, D., Ke, Y., and Zhang, W. (2015), “Model Selection and Structure Specification in Ultra-High Dimensional Generalised Semi-Varying Coefficient Models,” Annals of Statistics, 43, 2676–2705.
   Web of Science ®Google Scholar
• Li, R., and Liang H. (2008), “Variable Selection in Semiparametric Regression Modeling,” Annals of Statistics, 36, 261–286.
   PubMed Web of Science ®Google Scholar
• Li, R., and Nie, L. (2008), “Efficient Statistical Inference Procedures for Partially Nonlinear Models and Their Applications,” Biometrics, 64, 904–911. DOI: 10.1111/j.1541-0420.2007.00937.x.
   PubMed Web of Science ®Google Scholar
• Machado J.A. (1993), “Robust Model Selection and M-Estimation,” Econometric Theory, 9, 478–493. DOI: 10.1017/S0266466600007775.
   Web of Science ®Google Scholar
• Peng L. (2009), “A Practical Method for Analysing Heavy Tailed Data,” Canadian Journal of Statistics, 37, 235–248. DOI: 10.1002/cjs.10018.
   Web of Science ®Google Scholar
• Qian G., and Künsch H. (1996), “On Model Selection in Robust Linear Regression,” in Research report/Seminar für Statistik, Eidgenössische Technische Hochschule Zürich. Seminar für Statistik, Eidgenössische Technische Hochschule (ETH), Vol. 80.
   Google Scholar
• Quinn, B., and Thomson, P. (1991), “Estimating the Frequency of a Periodic Function,” Biometrika, 78, 65–74. DOI: 10.1093/biomet/78.1.65.
   Web of Science ®Google Scholar
• Rice J. A., and Rosenblatt, M. (1988), “On Frequency Estimation,” Biometrika, 75, 477–484. DOI: 10.1093/biomet/75.3.477.
   Web of Science ®Google Scholar
• Robinson, P. M. (1984), “Robust Nonparametric Autoregression,” in Robust and Nonlinear Time Series Analysis, eds. J. Franke, W. Härdle, and D. Martin D, New York: Springer, pp. 247–255.
   Google Scholar
• Shi, P., and Zheng, Z. (1995), “Rates of Convergence of M-Estimators for Partly Linear Models Involving Time Series,” Science in China (Scientia Sinica), Series A, 5, 533–541.
   Google Scholar
• Sun, Y., Hart, J. D., and Genton, M. G. (2012), “Nonparametric Inference for Periodic Sequences,” Technometrics, 54, 83–96. DOI: 10.1080/00401706.2012.650499.
   Web of Science ®Google Scholar
• Vogt, M. (2012), “Nonparametric Regression for Locally Stationary Time Series,” Annals of Statistics, 40, 2601–2633.
   Web of Science ®Google Scholar
• Vogt, M., and Linton, O. (2014), “Nonparametric Estimation of a Periodic Sequence in the Presence of a Smooth Trend,” Biometrika, 101, 121–140. DOI: 10.1093/biomet/ast051.
   Web of Science ®Google Scholar
• Walker A. (1971), “On the Estimation of a Harmonic Component in a Time Series With Stationary Independent Residuals,” Biometrika, 58, 21–36. DOI: 10.1093/biomet/58.1.21.
   Web of Science ®Google Scholar
• Wu Y., and Zen M. M. (1999), “A Strongly Consistent Information Criterion for Linear Model Selection Based on M-Estimation,” Probability Theory and Related Fields, 113, 599–625. DOI: 10.1007/s004400050219.
   Web of Science ®Google Scholar
• Xia, Y. (2006), “Asymptotic Distributions for Two Estimators of the Single-Index Model,” Econometric Theory, 22, 1112–1137. DOI: 10.1017/S0266466606060531.
   Web of Science ®Google Scholar
• Xia, Y. (2007), “A Constructive Approach to the Estimation of Dimension Reduction Directions,” Annals of Statistics, 35, 2654 – 2690.
   Web of Science ®Google Scholar
• Xia, Y. (2009), “A Note on the Back-Fitting Estimation of Additive Models,” Bernoulli, 15, 1148–1153.
   Web of Science ®Google Scholar
• Zhang W., Fan J., and Sun Y. (2009), “A Semiparametric Model for Cluster Data,” Annals of Statistics, 37, 2377–2408.
   PubMed Web of Science ®Google Scholar