Get access

TRANSFORMED POLYNOMIALS FOR NONLINEAR AUTOREGRESSIVE MODELS OF THE CONDITIONAL MEAN

Authors

  • Francisco Blasques

    Corresponding author
    1. Department of Econometrics, VU University Amsterdam, Amsterdam, The Netherlands
    2. Department of Finance, VU University Amsterdam, Amsterdam, The Netherlands
    3. Tinbergen Institute, Rotterdam, The Netherlands
    • Correspondence to: Francisco Blasques, VU University Amsterdam, FEWEB/FIN, de Boelelaan 1105, 1081 HV Amsterdam, The Netherlands. E-mail: f.blasques@vu.nl

    Search for more papers by this author

Abstract

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.

Ancillary