Linear Programming-Based Estimators in Nonnegative Autoregression

18 Pages Posted: 1 Sep 2015 Last revised: 18 Dec 2015

Date Written: August 11, 2015


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.

Keywords: robust estimation, linear programming estimator, strong convergence, nonlinear nonnegative autoregression, dependent non-identically distributed errors, heavy-tailed errors

JEL Classification: C13, C14, C22, C51, C58

Suggested Citation

Preve, Daniel P. A., Linear Programming-Based Estimators in Nonnegative Autoregression (August 11, 2015). Journal of Banking & Finance, Vol. 61, 2015, Available at SSRN:

Daniel P. A. Preve (Contact Author)

Singapore Management University ( email )

90 Stamford Road
Singapore, 178903

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