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Linear programming-based estimators in nonnegative autoregression

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Abstract

This note studies robust estimation of the autoregressive (AR) parameter in a nonlinear, nonnegative AR model driven by nonnegative errors. It is shown that a linear programming estimator (LPE), considered by Nielsen and Shephard (2003) among others, remains consistent under severe model misspecification. Consequently, the LPE can be used to test for, and seek sources of, misspecification when a pure autoregression cannot satisfactorily describe the data generating process, and to isolate certain trend, seasonal or cyclical components. Simple and quite general conditions under which the LPE is strongly consistent in the presence of serially dependent, non-identically distributed or otherwise misspecified errors are given, and a brief review of the literature on LP-based estimators in nonnegative autoregression is presented. Finite-sample properties of the LPE are investigated in an extensive simulation study covering a wide range of model misspecifications. A small scale empirical study, employing a volatility proxy to model and forecast latent daily return volatility of three major stock market indexes, illustrates the potential usefulness of the LPE.

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  • Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.
    • Handle: RePEc:eee:jbfina:v:61:y:2015:i:s2:p:s225-s234
    DOI: 10.1016/j.jbankfin.2015.08.010
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    Cited by:

    1. Anders Eriksson & Daniel P. A. Preve & Jun Yu, 2019. "Forecasting Realized Volatility Using a Nonnegative Semiparametric Model," JRFM, MDPI, vol. 12(3), pages 1-23, August.
    2. Shu, Yin & Feng, Qianmei & Liu, Hao, 2019. "Using degradation-with-jump measures to estimate life characteristics of lithium-ion battery," Reliability Engineering and System Safety, Elsevier, vol. 191(C).

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    More about this item

    Keywords

    Robust estimation; Linear programming estimator; Strong convergence; Nonlinear nonnegative autoregression; Dependent non-identically distributed errors; Heavy-tailed errors;
    All these keywords.

    JEL classification:

    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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