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TRANSFORMED POLYNOMIALS FOR NONLINEAR AUTOREGRESSIVE MODELS OF THE CONDITIONAL MEAN
Author(s) -
Blasques Francisco
Publication year - 2014
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12060
Subject(s) - mathematics , autoregressive model , estimator , conditional expectation , polynomial , strong consistency , asymptotic distribution , bounded function , series (stratigraphy) , consistency (knowledge bases) , ergodic theory , autoregressive conditional heteroskedasticity , star model , monte carlo method , econometrics , autoregressive integrated moving average , discrete mathematics , pure mathematics , time series , statistics , mathematical analysis , volatility (finance) , paleontology , biology
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.