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Estimation in nonlinear time series models


  • Tjøstheim, Dag


A general framework for analyzing estimates in nonlinear time series is developed. General conditions for strong consistency and asymptotic normality are derived both for conditional least squares and maximum likelihood types estimates. Ergodie strictly stationary processes are studied in the first part and certain nonstationary processes in the last part of the paper. Examples are taken from most of the usual classes of nonlinear time series models.

Suggested Citation

  • Tjøstheim, Dag, 1986. "Estimation in nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 251-273, February.
  • Handle: RePEc:eee:spapps:v:21:y:1986:i:2:p:251-273

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    Cited by:

    1. Carlo Grillenzoni, 1997. "Optimized adaptive prediction," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(1), pages 37-58, April.
    2. Addo, Peter Martey & Billio, Monica & Guégan, Dominique, 2014. "The univariate MT-STAR model and a new linearity and unit root test procedure," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 4-19.
    3. Meitz, Mika & Saikkonen, Pentti, 2011. "Parameter Estimation In Nonlinear Ar–Garch Models," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1236-1278, December.
    4. Tjøstheim, Dag & Hufthammer, Karl Ove, 2013. "Local Gaussian correlation: A new measure of dependence," Journal of Econometrics, Elsevier, vol. 172(1), pages 33-48.
    5. Liebscher, Eckhard, 2003. "Strong convergence of estimators in nonlinear autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 247-261, February.
    6. Jose, K.K. & Tomy, Lishamol & Sreekumar, J., 2008. "Autoregressive processes with normal-Laplace marginals," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2456-2462, October.
    7. Kilian, Lutz & Taylor, Mark P., 2003. "Why is it so difficult to beat the random walk forecast of exchange rates?," Journal of International Economics, Elsevier, vol. 60(1), pages 85-107, May.
    8. Thavaneswaran, A. & Peiris, Shelton, 1996. "Nonparametric estimation for some nonlinear models," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 227-233, July.
    9. Thavaneswaran, A. & Peiris, Shelton, 1998. "Hypothesis testing for some time-series models: a power comparison," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 151-156, June.
    10. Amano, Tomoyuki & Taniguchi, Masanobu, 2008. "Asymptotic efficiency of conditional least squares estimators for ARCH models," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 179-185, February.
    11. Hassan Bakouch & Miroslav Ristić, 2010. "Zero truncated Poisson integer-valued AR(1) model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 265-280, September.
    12. Sarno, Lucio & Taylor, Mark P. & Chowdhury, Ibrahim, 2004. "Nonlinear dynamics in deviations from the law of one price: a broad-based empirical study," Journal of International Money and Finance, Elsevier, vol. 23(1), pages 1-25, February.
    13. Taylor, Mark P. & Peel, David A., 2000. "Nonlinear adjustment, long-run equilibrium and exchange rate fundamentals," Journal of International Money and Finance, Elsevier, vol. 19(1), pages 33-53, February.
    14. Chandra, S. Ajay & Taniguchi, Masanobu, 2003. "Asymptotics of rank order statistics for ARCH residual empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 301-324, April.
    15. Chabot-Hallé, Dominique & Duchesne, Pierre, 2008. "Diagnostic checking of multivariate nonlinear time series models with martingale difference errors," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 997-1005, June.
    16. Carlo Grillenzoni, 2000. "Time-Varying Parameters Prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(1), pages 108-122, March.
    17. Thavaneswaran, A. & Peiris, Shelton, 2003. "Generalized smoothed estimating functions for nonlinear time series," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 51-56, October.
    18. Juan Carlos Escanciano, 2005. "On the Asymptotic Power Properties of Specification Tests for Dynamic Parametric Regressions," Faculty Working Papers 07/05, School of Economics and Business Administration, University of Navarra.
    19. Wagner Barreto-Souza & Marcelo Bourguignon, 2015. "A skew INAR(1) process on $${\mathbb {Z}}$$ Z," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 189-208, April.


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