Parameter Estimation With Out-of-Sample Objective

53 Pages Posted: 24 May 2018

See all articles by Peter Reinhard Hansen

Peter Reinhard Hansen

University of North Carolina (UNC) at Chapel Hill - Department of Economics; Copenhagen Business School, Finance; Aarhus University - CREATES

Elena-Ivona Dumitrescu

CEROS, Paris Nanterre University

Date Written: March 13, 2018

Abstract

We study parameter estimation from the sample X, when the objective is to maximize the expected value of a criterion function, Q, for a distinct sample, Y. This is the situation that arises when a model is estimated for the purpose of describing other data than those used for estimation. The motivated for much estimation has this form, with forecasting problems being a prime example. A natural estimator is the innate estimator that maximizes Q(X;\theta.) wrt. \theta. While the innate estimator has certain advantages, we show that the asymptotically efficient estimator is defined from a likelihood function in conjunction with Q. The likelihood-based estimator is, however, fragile, as misspecification is harmful in two ways. First, the likelihood-based estimator may be inefficient under misspecification. Second, and more importantly, the likelihood approach requires a parameter transformation that depends on the truth, causing an improper mapping to be used under misspecification. The theoretical results are illustrated with two applications comprising asymmetric loss and multi-step forecasting, respectively.

Keywords: Estimation, Forecasting, Out-of-Sample, LinEx Loss, Multi-Step Forecasting

JEL Classification: C18, C13, C51, C52

Suggested Citation

Hansen, Peter Reinhard and Dumitrescu, Elena-Ivona, Parameter Estimation With Out-of-Sample Objective (March 13, 2018). Available at SSRN: https://ssrn.com/abstract=3178896 or http://dx.doi.org/10.2139/ssrn.3178896

Peter Reinhard Hansen (Contact Author)

University of North Carolina (UNC) at Chapel Hill - Department of Economics ( email )

Chapel Hill, NC 27599
United States

HOME PAGE: http://https://sites.google.com/site/peterreinhardhansen/

Copenhagen Business School, Finance ( email )

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Elena-Ivona Dumitrescu

CEROS, Paris Nanterre University

200 avenue de la République
NANTERRE, 92000
France

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