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Asymptotic Theory For Empirical Similarity Models

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  • Lieberman, Offer

Abstract

We consider the stochastic process null , t = 2, …, n , where s ( x , x ) is a similarity function between the t th and the i th observations and { ε } is a random disturbance term. This process was originally axiomatized by Gilboa, Lieberman, and Schmeidler (2006, Review of Economics and Statistics 88, 433–444) as a way by which agents, or even nature, reason. In the present paper, consistency and the asymptotic distribution of the quasi-maximum likelihood estimator of the parameters of the model are established. Connections to other models and techniques are drawn. In its general form, the model does not fall within any class of nonstationary econometric models for which asymptotic theory is available. For this reason, the developments in this paper are new and nonstandard.

Suggested Citation

  • Lieberman, Offer, 2010. "Asymptotic Theory For Empirical Similarity Models," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1032-1059, August.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1032-1059_99
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    Cited by:

    1. Lieberman, Offer & Phillips, Peter C.B., 2017. "A multivariate stochastic unit root model with an application to derivative pricing," Journal of Econometrics, Elsevier, vol. 196(1), pages 99-110.
    2. Golosnoy, Vasyl & Hamid, Alain & Okhrin, Yarema, 2014. "The empirical similarity approach for volatility prediction," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 321-329.
    3. Kapetanios, George & Mitchell, James & Shin, Yongcheol, 2014. "A nonlinear panel data model of cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 179(2), pages 134-157.
    4. Offer Lieberman & Peter C. B. Phillips, 2014. "Norming Rates And Limit Theory For Some Time-Varying Coefficient Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 592-623, November.
    5. Hamid, Alain & Heiden, Moritz, 2015. "Forecasting volatility with empirical similarity and Google Trends," Journal of Economic Behavior & Organization, Elsevier, vol. 117(C), pages 62-81.
    6. Keita Kinjo & Shinya Sugawara, 2014. "An Empirical Analysis for a Case-based Decision to Watch Japanese TV dramas," CIRJE F-Series CIRJE-F-940, CIRJE, Faculty of Economics, University of Tokyo.
    7. Oscar Melo & Carlos Melo & Jorge Mateu, 2015. "Distance-based beta regression for prediction of mutual funds," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 83-106, January.
    8. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.

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