Spline estimation of partially linear regression models for time series with correlated errors

References

• Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (6):716–23. doi:10.1109/TAC.1974.1100705.
   Web of Science ®Google Scholar
• Bosq, D., and J. Shen. 1998. Estimation of an autoregressive semiparametric model with exogenous variables. Journal of Statistical Planning and Inference 68 (1):105–27. doi:10.1016/S0378-3758(97)00137-7.
   Web of Science ®Google Scholar
• Box, G. E. P., and G. M. Jenkins. 1970. Time series analysis: Forecasting and control. San Francisco: Holden-Day.
   Google Scholar
• Chen, R., and R. S. Tsay. 1993. Functional coefficient autoregressive models. Journal of the American Statistic Association 88 (421):298–308.
   Web of Science ®Google Scholar
• Chen, R., L. Yang, and C. Hafner. 2004. Nonparametric multi-step ahead prediction in time series analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 66 (3):669–86. doi:10.1111/j.1467-9868.2004.04664.x.
   Google Scholar
• Damon, J., and S. Guillas. 2005. Estimation and simulation of autoregressive hilbertian processes with exogenous variables. Statistical Inference for Stochastic Processes 8 (2):185–204. doi:10.1007/s11203-004-1031-6.
   Google Scholar
• De Boor, C. 2001. A practical guide to splines. New York: Springer-Verlag.
   Google Scholar
• DeVore, R. A., and G. G. Lorentz. 1993. Constructive approximation. Heidelberg: Springer-Verlag.
   Google Scholar
• Engle, R. F., C. W. J. Granger, J. Rice, and A. Weiss. 1986. Semiparametric estimates of the relation between weather and electricity sales. Journal of the American Statistical Association 81 (394):310–20. doi:10.1080/01621459.1986.10478274.
   Web of Science ®Google Scholar
• Fan, J., and Q. Yao. 2003. Nonlinear time series: Nonparametric and parametric methods. New York: Springer-Verlag.
   Google Scholar
• Gao, J. 2007. Nonlinear time series: Semiparametric and nonparametric methods. London: Chapman & Hall.
   Google Scholar
• Gao, J., and H. Liang. 1995. Asymptotic normality of pseudo-LS estimator for partially linear autoregressive models. Statistics & Probability Letters 23 (1):27–34. doi:10.1016/0167-7152(94)00091-L.
   Web of Science ®Google Scholar
• Granger, C. W. J., and T. Teräsvirta. 1993. Modelling non-linear economic relationships. Oxford: Oxford University Press.
   Google Scholar
• Härdle, W., H. Liang, and J. Gao. 2000. Partially linear models. Heidelberg: Physica-Verlag.
   Google Scholar
• Haggan, V., and T. Ozaki. 1981. Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model. Biometrika 68 (1):189–96. doi:10.1093/biomet/68.1.189.
   Web of Science ®Google Scholar
• Huang, J. Z., and H. Shen. 2004. Functional coefficient regression models for non-linear time series: A polynomial spline approach. Scandinavian Journal of Statistics 31 (4):515–34. doi:10.1111/j.1467-9469.2004.00404.x.
   Web of Science ®Google Scholar
• Huang, J. Z., and L. Yang. 2004. Identification of non-linear additive autoregressive models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 66 (2):463–77. doi:10.1111/j.1369-7412.2004.05500.x.
   Google Scholar
• Li, D., G. Li, and J. You. 2014. Significant variable selection and autoregressive order determination for time-Series partially linear models. Journal of Time Series Analysis 35 (5):478–90. doi:10.1111/jtsa.12077.
   Web of Science ®Google Scholar
• Liang, H. 1996. Second order asymptotic efficiency in a partly autoregressive model. Systems Science Mathematical Sciences 9 (2):164–70.
   Google Scholar
• Montoril, M. H., P. A. Morettin, and C. Chiann. 2014. Spline estimation of functional coefficient regression models for time series with correlated errors. Statistics & Probability Letters 92:226–31. doi:10.1016/j.spl.2014.05.021.
   Web of Science ®Google Scholar
• Montoril, M. H., P. A. Morettin, and C. Chiann. 2018. Wavelet estimation of functional coefficient regression models. International Journal of Wavelets Multiresolution & Information Processing 16 (1):8–39.
   Web of Science ®Google Scholar
• Saarta, P., J. Gao, and N. H. Kim. 2014. Semiparametric methods in nonlinear time series analysis: A selective review. Journal of Nonparametric Statistics 26 (1):141–69. doi:10.1080/10485252.2013.840724.
   Web of Science ®Google Scholar
• Schwarz, G. 1978. Estimating the dimension of a model. The Annals of Statistics 6 (2):461–4. doi:10.1214/aos/1176344136.
   Web of Science ®Google Scholar
• Stone, C. J. 1985. Additive regression and other nonparametric models. The Annals of Statistics 13 (2):689–705. doi:10.1214/aos/1176349548.
   Web of Science ®Google Scholar
• Su, L., and A. Ullah. 2006. More efficient estimation in nonparametric regression with nonparametric autocorrelated errors. Econometric Theory 22 (01):98–126. doi:10.1017/S026646660606004X.
   Google Scholar
• Tong, H. 1983. Threshold models in non-linear time series analysis. In: Lecture notes in statistics. New York: Springer-Verlag.
   Google Scholar
• Tong, H. 1990. Non-linear time series: A dynamical system approach. Oxford: Oxford University Press.
   Google Scholar
• Wu, X., Z. Tian, and S. Han. 2007. Spline estimation for partially linear autoregressive models with an exogenous variable. Chinese Annals of Mathematics Series A 28 (3):277–386.
   Google Scholar
• Wu, X., Z. Tian, and H. Wang. 2009. Polynomial spline estimation for nonparametric (auto-) regressive models. Studia Scientiarum Mathematicarum Hungarica 46 (4):515–38. doi:10.1556/sscmath.2009.1105.
   Web of Science ®Google Scholar
• Yee, T., and J. Gao. 2000. Adaptive estimation in partially linear autoregressive models. Canadian Journal of Statistics 28 (3):571–86. doi:10.2307/3315966.
   Web of Science ®Google Scholar