Abstract
The recent development of nonlinear time series analysis is primarily due to the efforts to overcome the limitations of linear models such as the autoregressive moving-average models of Box and Jenkins (1976) in real applications. It is also attributed to the development of nonlinear/nonparamctric regression techniques which provides many useful tools. Advanced computational power and easy-to-use advanced software and graphics such as S-Plus and XploRe make all of these possible.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Auestad, B. and Tjøstheim, D. (1990). Identification of nonlinear time series: First order characterization and order estimation, Biometrika 77 (4): 669–687.
Basawa, I.V. and Prakasa Rao, B.L.S. (1980). Statistical Inference for Stochastic Processes, Academic Press, London.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity, Journal of Econometrics 31(3): 307–327.
Bollerslev, T., Chou, R.Y. and Kroner, K.F. (1992). Arch modelling in finance: A review of the theory and empirical evidence, Journal of Econometrics 52 (1): 5–59.
Box, G.E.P. and Jenkins, G.M. (1976). Time Series Analysis: Foretasting and Control, Holden-Day, San Fransisco.
Breiman, L. and Friedman, J.H. (1985). Estimating optimal transformations for multiple regression and correlations (with discussion), Journal of the American Statistical Association 80 (391): 580–619.
Chan, K.S. (1990). Testing for threshold autoregression, Annals of Statistics 18 (4): 1886–1891.
Chen, R. (1994). A nonparametric predictor for nonlinear time series, Technical report, Department of Statistics, Texas A&M University, College Station.
Chen, R. and Tsay, R.S. (1993a). Functional-coefficient autoregressive models, Journal of the American Statistical Association 88 (421): 298–308.
Chen, R. and Tsay, R.S. (1993b). Nonlinear additive ARX models, Journal of the American Statistical Association 88 (423): 955–967.
Cleveland, W.S. and Devlin, S.J. (1988). Locally weighted regression: An approach to regression analysis by local fitting, Journal of the American Statistical Association 83 (403): 596–610.
Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation, Econometrica 50 (4): 987–1007.
Feller. W. (1966). An Introduction to Probability Theory and Its Application. Vol. 2, John Wiley & Sons, New York.
Friedman, J.H. (1991). Multivariate adaptive regression splines (with discussion), Annals of Statistics 19 (1): 1–141.
Granger, C.W.J, and Anderson, A.P. (1978). An Introduction to Bilinear Time Series Models, Vandenhoeck & Ruprecht, Göttingen und Zürich.
Granger, C.W.J, and Teräsvirta, T. (1993). Modelling Nonlinear Economic Relationships, Academic Press. Oxford.
Haggan, V. and Ozaki, T. (1981). Modeling nonlinear vibrations using an amplitude-dependent autoregressive time series model. Biometrika 68 (1): 189–196.
Hall, P. and Heyde, C.C. (1980). Martingale. Limit Theory and Its Applications. Academic Press, New York.
Härdle, W. and Vieu, P. (1992). Kernel regression smoothing of time series. Journal of Time Series Analysis 13 (3): 209–232.
Hastie, T.J. and Tibshirani. R.J. (1990). Generalized Additive Models, Vol. 43 of Monographs on Statistics and Applied Probability, Chapman and Hall. London.
Hinich. M.J. (1982). Testing for gaussianity and linearity of a stationary time series, Journal of Time Series Analysis 3 (3): 169–170.
Hinich, M.J. and Patterson, D.M. (1985). Identification of the coefficient in a nonlinear time series of the quadratic type, Journal of Econometrics 30 (3): 269–288.
Hjellvik, V. and Tjøstheim, D. (1994). Nonparametric tests of linearity for time series. Biometrika. To appear.
Jones, D.A. (1978). Nonlinear autoregressive processes. Proceedings of the Royal Society of London, Series A 360: 71–95.
Keenan, D.M. (1985). A Tukey nonadditivity-type test for time series nonlinearity, Biometrika 72 (1): 39–44.
Klimko, L.A. and Nelson, P.I. (1978). On conditional least squares estimation for stochastic processes, Annals of Statistics 6 (3): 629–642.
Lai, T.L. and Wei. C.Z. (1983). Asymptotic properties of general autoregressive models and strong consistency of the least squares estimates of their parameters, Journal of Multivariate Analysis 13 (1): 1–23.
Lewis, P.A.W. and Stevens, G. (1991). Nonlinear modeling of time series using multivariate adaptive regression splines (mars), Journal of the American Statistical Association 86 (416): 864–877.
Luukkonen, R., Saikkonen, P. and Teräsvirta. T. (1988). Testing linearity against smooth transition autoregressive models, Biometrika 75 (3): 491–499.
Pemberton, J. (1987). Exact least squares multi-step prediction from nonlinear autoregressive models. Journal of Time Series Analysis 8 (4): 443–448.
Petruccelli, J. and Davies, N. (1986). A portmanteau test for self-exciting threshold autoregressive-type nonlinearity in time series, Biometrika 73 (3): 687–694.
Priestley, M.B. (1988). Non-linear and Non-stationary Time Series Analysis, Academic Press, New York.
Robinson, P.M. (1977). The estimation of a nonlinear moving average model, Stochastic Processes and Their Applications 5: 81–90.
Robinson, P.M. (1983). Non-parametric estimation for time series models, Journal of Time Series Analysis 4 (3): 185–208.
Subba Rao. T. (1981). On the theory of bilinear time series models, Journal of the Royal Statistical Society, Series B 43 (2): 244–255.
Subba Rao, T. and Gabr, M.M. (1980). An introduction to bispectral analysis and bilinear time series models, Vol. 24 of Lecture Notes in Statistics, Springer-Verlag, New York.
Sugihara, G. and May, R.M. (1990). Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series, Nature 344 (6268): 734–741.
Tibshirani. R.J. (1988). Estimating transformations for regression via additivity and variance stabilization, Journal of the American Statistical Association 83 (402): 391–405.
Tjøstheim, D. (1986). Estimation in nonlinear time series models, Stochastic Processes and Their Applications 21: 251–273.
Tong, H. (1978). On a threshold model, in C.H. Chen (ed.), Pattern Recognition and Signal Processing, Sijthoff and Noordholf. The Netherlands.
Tong, H. (1983). Threshold Models in Nonlinear Time Series Analysis, Vol. 21 of Lecture Notes in Statistics, Springer-Verlag, Heidelberg.
Tong, H. (1990). Nonlinear Time Series Analysis: A Dynamic Approach, Oxford University Press, Oxford.
Truong, Y.K. (1993). A nonparametric framework for time series analysis, in D. Billinger, P. Caines, J. Geweke, E. Parzen. M. Rosenblatt and M.S. Taqqu (eds), New Directions in Time Series Analysis, Springer-Verlag, New York.
Tsay. R.S. (1986). Nonlinearity tests for time series, Biometrika 73 (2): 461–466.
Tsay, R.S. (1989). Testing and modeling threshold autoregressive processes, Journal of the American Statistical Association 84 (405): 231–240.
Tsay, R.S. (1991). Detecting and modeling nonlinearity in univariate time series analysis, Statistica Sinica 1 (2): 431 – 451.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Chen, R., Hafner, C. (1995). Nonlinear Time Series Analysis. In: XploRe: An Interactive Statistical Computing Environment. Statistics and Computing. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4214-7_14
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4214-7_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8699-8
Online ISBN: 978-1-4612-4214-7
eBook Packages: Springer Book Archive