Skip to main content

Part of the book series: Statistics and Computing ((SCO))

  • 247 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

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.

    Article  MathSciNet  Google Scholar 

  • Basawa, I.V. and Prakasa Rao, B.L.S. (1980). Statistical Inference for Stochastic Processes, Academic Press, London.

    MATH  Google Scholar 

  • Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity, Journal of Econometrics 31(3): 307–327.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Box, G.E.P. and Jenkins, G.M. (1976). Time Series Analysis: Foretasting and Control, Holden-Day, San Fransisco.

    Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Chan, K.S. (1990). Testing for threshold autoregression, Annals of Statistics 18 (4): 1886–1891.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, R. (1994). A nonparametric predictor for nonlinear time series, Technical report, Department of Statistics, Texas A&M University, College Station.

    Google Scholar 

  • Chen, R. and Tsay, R.S. (1993a). Functional-coefficient autoregressive models, Journal of the American Statistical Association 88 (421): 298–308.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, R. and Tsay, R.S. (1993b). Nonlinear additive ARX models, Journal of the American Statistical Association 88 (423): 955–967.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation, Econometrica 50 (4): 987–1007.

    Article  MathSciNet  MATH  Google Scholar 

  • Feller. W. (1966). An Introduction to Probability Theory and Its Application. Vol. 2, John Wiley & Sons, New York.

    Google Scholar 

  • Friedman, J.H. (1991). Multivariate adaptive regression splines (with discussion), Annals of Statistics 19 (1): 1–141.

    Article  MathSciNet  MATH  Google Scholar 

  • Granger, C.W.J, and Anderson, A.P. (1978). An Introduction to Bilinear Time Series Models, Vandenhoeck & Ruprecht, Göttingen und Zürich.

    MATH  Google Scholar 

  • Granger, C.W.J, and Teräsvirta, T. (1993). Modelling Nonlinear Economic Relationships, Academic Press. Oxford.

    MATH  Google Scholar 

  • Haggan, V. and Ozaki, T. (1981). Modeling nonlinear vibrations using an amplitude-dependent autoregressive time series model. Biometrika 68 (1): 189–196.

    Article  MathSciNet  MATH  Google Scholar 

  • Hall, P. and Heyde, C.C. (1980). Martingale. Limit Theory and Its Applications. Academic Press, New York.

    Google Scholar 

  • Härdle, W. and Vieu, P. (1992). Kernel regression smoothing of time series. Journal of Time Series Analysis 13 (3): 209–232.

    Article  MathSciNet  MATH  Google Scholar 

  • Hastie, T.J. and Tibshirani. R.J. (1990). Generalized Additive Models, Vol. 43 of Monographs on Statistics and Applied Probability, Chapman and Hall. London.

    Google Scholar 

  • Hinich. M.J. (1982). Testing for gaussianity and linearity of a stationary time series, Journal of Time Series Analysis 3 (3): 169–170.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Hjellvik, V. and Tjøstheim, D. (1994). Nonparametric tests of linearity for time series. Biometrika. To appear.

    Google Scholar 

  • Jones, D.A. (1978). Nonlinear autoregressive processes. Proceedings of the Royal Society of London, Series A 360: 71–95.

    Article  MATH  Google Scholar 

  • Keenan, D.M. (1985). A Tukey nonadditivity-type test for time series nonlinearity, Biometrika 72 (1): 39–44.

    Article  MathSciNet  MATH  Google Scholar 

  • Klimko, L.A. and Nelson, P.I. (1978). On conditional least squares estimation for stochastic processes, Annals of Statistics 6 (3): 629–642.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Luukkonen, R., Saikkonen, P. and Teräsvirta. T. (1988). Testing linearity against smooth transition autoregressive models, Biometrika 75 (3): 491–499.

    Article  MathSciNet  MATH  Google Scholar 

  • Pemberton, J. (1987). Exact least squares multi-step prediction from nonlinear autoregressive models. Journal of Time Series Analysis 8 (4): 443–448.

    Article  MathSciNet  Google Scholar 

  • Petruccelli, J. and Davies, N. (1986). A portmanteau test for self-exciting threshold autoregressive-type nonlinearity in time series, Biometrika 73 (3): 687–694.

    Article  MathSciNet  MATH  Google Scholar 

  • Priestley, M.B. (1988). Non-linear and Non-stationary Time Series Analysis, Academic Press, New York.

    Google Scholar 

  • Robinson, P.M. (1977). The estimation of a nonlinear moving average model, Stochastic Processes and Their Applications 5: 81–90.

    Article  MathSciNet  MATH  Google Scholar 

  • Robinson, P.M. (1983). Non-parametric estimation for time series models, Journal of Time Series Analysis 4 (3): 185–208.

    Article  MathSciNet  MATH  Google Scholar 

  • Subba Rao. T. (1981). On the theory of bilinear time series models, Journal of the Royal Statistical Society, Series B 43 (2): 244–255.

    MathSciNet  MATH  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Tibshirani. R.J. (1988). Estimating transformations for regression via additivity and variance stabilization, Journal of the American Statistical Association 83 (402): 391–405.

    Article  MathSciNet  Google Scholar 

  • Tjøstheim, D. (1986). Estimation in nonlinear time series models, Stochastic Processes and Their Applications 21: 251–273.

    Article  MathSciNet  Google Scholar 

  • Tong, H. (1978). On a threshold model, in C.H. Chen (ed.), Pattern Recognition and Signal Processing, Sijthoff and Noordholf. The Netherlands.

    Google Scholar 

  • Tong, H. (1983). Threshold Models in Nonlinear Time Series Analysis, Vol. 21 of Lecture Notes in Statistics, Springer-Verlag, Heidelberg.

    Google Scholar 

  • Tong, H. (1990). Nonlinear Time Series Analysis: A Dynamic Approach, Oxford University Press, Oxford.

    Google Scholar 

  • 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.

    Google Scholar 

  • Tsay. R.S. (1986). Nonlinearity tests for time series, Biometrika 73 (2): 461–466.

    Article  MathSciNet  MATH  Google Scholar 

  • Tsay, R.S. (1989). Testing and modeling threshold autoregressive processes, Journal of the American Statistical Association 84 (405): 231–240.

    Article  MathSciNet  MATH  Google Scholar 

  • Tsay, R.S. (1991). Detecting and modeling nonlinearity in univariate time series analysis, Statistica Sinica 1 (2): 431 – 451.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints 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

Publish with us

Policies and ethics