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Transformed Polynomials For Nonlinear Autoregressive Models Of The Conditional Mean

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  • Francisco Blasques

Abstract

type="main" xml:id="jtsa12060-abs-0001"> This article proposes a flexible set of transformed polynomial functions for modelling the conditional mean of autoregressive processes. These functions enjoy the same approximation theoretic properties of polynomials and, at the same time, ensure that the process is strictly stationary, is ergodic, has fading memory and has bounded unconditional moments. The consistency and asymptotic normality of the least-squares estimator is easily obtained as a result. A Monte Carlo study provides evidence of good finite sample properties. Applications in empirical time-series modelling, structural economics and structural engineering problems show the usefulness of transformed polynomials in a wide range of settings.

Suggested Citation

  • Francisco Blasques, 2014. "Transformed Polynomials For Nonlinear Autoregressive Models Of The Conditional Mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 218-238, May.
    • Handle: RePEc:bla:jtsera:v:35:y:2014:i:3:p:218-238
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    1. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
    2. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramirez & Martin Uribe, 2011. "Risk Matters: The Real Effects of Volatility Shocks," American Economic Review, American Economic Association, vol. 101(6), pages 2530-2561, October.
    3. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    4. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
    5. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    6. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
    7. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    8. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    9. Tjøstheim, Dag, 1986. "Estimation in nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 251-273, February.
    10. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2003. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Computing in Economics and Finance 2003 162, Society for Computational Economics.
    11. Karen E. Dynan, 2000. "Habit Formation in Consumer Preferences: Evidence from Panel Data," American Economic Review, American Economic Association, vol. 90(3), pages 391-406, June.
    12. K. S. Lim, 1987. "A Comparative Study Of Various Univariate Time Series Models For Canadian Lynx Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 161-176, March.
    13. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
    14. Den Haan, Wouter J. & De Wind, Joris, 2012. "Nonlinear and stable perturbation-based approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1477-1497.
    15. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
    16. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    17. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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    Cited by:

    1. Francisco (F.) Blasques & Marc Nientker, 2019. "Transformed Perturbation Solutions for Dynamic Stochastic General Equilibrium Models," Tinbergen Institute Discussion Papers 19-012/III, Tinbergen Institute, revised 09 Feb 2020.

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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