Functional-Coefficient Regression Models for Nonlinear Time Series

References

• An , H. Z. and Chen , S. G. 1997 . “A Note on the Ergodicity of Nonlinear Autoregressive Models” . Statistics and Probability Letters , 34 : 365 – 372 .
   Web of Science ®Google Scholar
• An , H. Z. and Huang , F. C. 1996 . “The Geometrical Ergodicity of Nonlinear Autoregressive Models” . Statistica Sinica , 6 : 943 – 956 .
   Web of Science ®Google Scholar
• Auestad , B. and Tjøstheim , D. 1990 . “Identification of Nonlinear Time Series: First-Order Characterization and Order Determination” . Biometrika , 77 : 669 – 687 .
   Web of Science ®Google Scholar
• Bollerslev , T. 1986 . “Generalized Autoregressive Conditional Heteroscedasticity” . Journal of Econometrics , 31 : 307 – 327 .
   Web of Science ®Google Scholar
• Box , G. E. P. and Jenkins , G. M. 1970 . Time Series Analysis, Forecasting, and Control , San Francisco : Holden Day .
   Google Scholar
• Brumback , B. and Rice , J. 1998 . “Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves” . Journal of the American Statistical Association , 93 : 961 – 976 . (with discussion)
   Web of Science ®Google Scholar
• Chen , R. and Tsay , R. S. 1993 . “Functional-Coefficient Autoregressive Models” . Journal of the American Statistical Association , 88 : 298 – 308 .
   Web of Science ®Google Scholar
• Cleveland , W. S. , Grosse , E. and Shyu , W. M. 1992 . “Local Regression Models,” . In Statistical Models in S , Edited by: Chambers , J. M. and Hastie , T. J. 309 – 376 . Pacific Grove , CA : Wadsworth & Brooks/Cole .
   Google Scholar
• Dahlhaus , R. 1989 . “Efficient Parameter Estimation for Self-Similar Processes” . The Annals of Statistics , 17 : 1749 – 1766 .
   Web of Science ®Google Scholar
• Engle , R. F. 1982 . “Autoregressive Conditional Heteroscedasticity With Estimates of the Variance of U.K. Inflation” . Econometrica , 50 : 987 – 1008 .
   Web of Science ®Google Scholar
• Engle , R. F. and Granger , C. W. J. 1987 . “Cointegration and Error Correction: Representation, Estimation and Testing” . Econometrica , 55 : 251 – 276 .
   Web of Science ®Google Scholar
• Fan , J. 1993 . “Local Linear Regression Smoothers and Their Minimax” . The Annals of Statistics , 21 : 196 – 216 .
   Web of Science ®Google Scholar
• Fan , J. and Gijbels , I. 1995 . “Data-Driven Bandwidth Selection in Local Polynomial Fitting: Variable Bandwidth Spatial Adaptation” . Journal of the Royal Statistical Society , 57 : 371 – 394 . Ser. B
   Google Scholar
• Fan , J. and Gijbels , I. 1996 . Local Polynomial Modeling and Its Applications , London : Chapman and Hall .
   Google Scholar
• Fan , J. , Yao , Q. and Cai , Z. 2000 . “Adaptive Varying-Coefficient Linear Models,” unpublished manuscript
   Google Scholar
• Fan , J. , Zhang , C. and Zhang , J. 1999 . “Sieve Likelihood Ratio Statistics and Wilks Phenomenon,” , Los Angeles : Department of Statistics, University of California . technical report
   Google Scholar
• Fan , J. and Zhang , W. 1999 . “Statistical Estimation in Varying-Coefficient Models” . The Annals of Statistics , 27 : 1491 – 1518 .
   Web of Science ®Google Scholar
• Ghaddar , D. K. and Tong , H. 1981 . “Data Transformation and Self-Exciting Threshold Autoregression” . Journal of the Royal Statistical Society , 30 : 238 – 248 . Ser. C
   Google Scholar
• Gorodetskii , V. V. 1977 . “On the Strong Mixing Property for Linear Sequences” . Theory of Probability and Its Applications , 22 : 411 – 413 .
   Web of Science ®Google Scholar
• Granger , C. W. J. and Joyeux , R. 1980 . “An Introduction to Long-Memory Time Series Models and Fractional Differencing” . Journal of Time Series Analysis , 1 : 15 – 29 .
   Google Scholar
• Granger , C. W. J. and Teräsvirta , T. 1993 . Modeling Nonlinear Economic Relationships , Oxford , , U.K. : Oxford University Press .
   Google Scholar
• Haggan , V. and Ozaki , T. 1981 . “Modeling Nonlinear Vibrations Using an Amplitude-Dependent Autoregressive Time Series Model” . Biometrika , 68 : 189 – 196 .
   Web of Science ®Google Scholar
• Hall , P. and Heyde , C. C. 1980 . Martingale Limit Theory and Its Applications , New York : Academic Press .
   Google Scholar
• Hannan , E. J. and Deistler , M. 1988 . The Statistical Theory of Linear Systems , New York : Wiley .
   Google Scholar
• Härdle , W. , Lütkepohl , H. and Chen , R. 1997 . “A Review of Nonparametric Time Series Analysis” . International Statistical Review , 65 : 49 – 72 .
   Web of Science ®Google Scholar
• Hästie , T. J. and Loader , C. 1993 . “Local Regression: Automatic Kernel Carpentry” . Statistical Science , 8 : 120 – 143 . (with discussion)
   Web of Science ®Google Scholar
• Hastie , T. J. and Tibshirani , R. J. 1993 . “Varying-Coefficient Models” . Journal of the Royal Statistical Society , 55 : 757 – 796 . (with discussion), Ser. B
   Google Scholar
• Hoover , D. R. , Rice , J. A. , Wu , C. O. and Yang , L. P. 1998 . “Nonparametric Smoothing Estimates of Time-Varying Coefficient Models With Longitudinal Data” . Biometrika , 85 : 809 – 822 .
   Web of Science ®Google Scholar
• Ibragimov , I. A. and Linnik , Yu. V. 1971 . Independent and Stationary Sequences of Random Variables , Groningen , , The Netherlands : Walters-Noordhoff .
   Google Scholar
• Kreiss , J. P. , Neumann , M. and Yao , Q. 1998 . “Bootstrap Tests for Simple Structures in Nonparametric Time Series Regression,” unpublished manuscript
   Google Scholar
• Masry , E. and Fan , J. 1997 . “Local Polynomial Estimation of Regression Functions for Mixing Processes” . Scandinavian Journal of Statistics , 24 : 165 – 179 .
   Web of Science ®Google Scholar
• Masry , E. and Tjøtheim , D. 1995 . “Nonparametric Estimation and Identification of Nonlinear ARCH Time Series: Strong Convergence and Asymptotic Normality” . Econometric Theory , 11 : 258 – 289 .
   Web of Science ®Google Scholar
• Masry , E. and Tjøtheim , D. 1997 . “Additive Nonlinear ARX Time Series and Projection Estimates” . Econometric Theory , 13 : 214 – 252 .
   Web of Science ®Google Scholar
• Nicholls , D. F. and Quinn , B. G. 1982 . Random Coefficient Autoregressive Models: An Introduction , New York : Springer-Verlag . Lecture Notes in Statistics 11
   Google Scholar
• Ozaki , T. 1982 . “The Statistical Analysis of Perturbed Limit Cycle Processes Using Nonlinear Time Series Models” . Journal of Time Series Analysis , 3 : 29 – 41 .
   Google Scholar
• Ramsay , J. O. and Silverman , B. W. 1997 . Functional Data Analysis , Berlin : Springer-Verlag .
   Google Scholar
• Ruppert , D. , Sheather , S. J. and Wand , M. P. 1995 . “An Effective Bandwidth Selection for Local Least Squares Regression” . Journal of the American Statistical Association , 90 : 1257 – 1270 .
   Web of Science ®Google Scholar
• Ruppert , D. and Wand , M. P. 1994 . “Multivariate Weighted Least Squares Estimation” . The Annals of Statistics , 22 : 1346 – 1370 .
   Web of Science ®Google Scholar
• Shao , Q. and Yu , H. 1996 . “Weak Convergence for Weighted Empirical Processes of Dependent Sequences” . The Annals of Probability , 24 : 2098 – 2127 .
   Web of Science ®Google Scholar
• Stenseth , N. C. , Falck , W. , Chan , K. S. , Bjørnstad , O. N. , O'Donoghue , M. , Tong , H. , Boonstra , R. , Boutin , S. , Krebs , C. J. and Yoccoz , N. G. 1998 . “From Ecological Patterns to Ecological Processes: Phase-and Density-Dependencies in Canadian Lynx Cycle” . Proceedings of National Academy of Science, Washington , 95 : 15430 – 15435 .
   PubMed Web of Science ®Google Scholar
• Sun , Z. 1984 . “Asymptotic Unbiased and Strong Consistency for Density Function Estimator” . Acta Mathematica Sinica , 27 : 769 – 782 .
   Google Scholar
• Tiao , G. C. and Tsay , R. S. 1994 . “Some Advances in Nonlinear and Adaptive Modeling in Time Series” . Journal of Forecasting , 13 : 109 – 131 .
   Web of Science ®Google Scholar
• Tjøstheim , D. 1994 . “Non-Linear Time Series: A Selective Review” . Scandinavian Journal of Statistics , 21 : 97 – 130 .
   Web of Science ®Google Scholar
• Tong , H. 1990 . Nonlinear Time Series: A Dynamical System Approach , Oxford , , U.K. : Oxford University Press .
   Google Scholar
• Tong , H. 1995 . “A Personal Overview of Non-Linear Time Series Analysis From a Chaos Perspective” . Scandinavian Journal of Statistics , 22 : 399 – 445 . (with discussion)
   Web of Science ®Google Scholar
• Volkonskii , V. A. and Rozanov , Yu. A. 1959 . “Some Limit Theorems for Random Functions. I” . Theory of Probability and Its Applications , 4 : 178 – 197 .
   Google Scholar
• Withers , C. S. 1981 . “Conditions for Linear Processes to be Strong Mixing” . Zeitschrift fur Wahrscheinlichkeitstheorie Verwandte Gebiete , 57 : 477 – 480 .
   Web of Science ®Google Scholar
• Yao , Q. and Tong , H. 1995 . “On Initial-Condition Sensitivity and Prediction in Nonlinear Stochastic Systems” . Bulletin of the International Statistical Institute , IP 10.3 : 395 – 412 .
   Google Scholar