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Threshold estimation of Markov models with jumps and interest rate modeling

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  • Mancini, Cecilia
  • Renò, Roberto

Abstract

We reconstruct the level-dependent diffusion coefficient of a univariate semimartingale with jumps which is observed discretely. The consistency and asymptotic normality of our estimator are provided in the presence of both finite and infinite activity (finite variation) jumps. Our results rely on kernel estimation, using the properties of the local time of the data generating process, and the fact that it is possible to disentangle the discontinuous part of the state variable through those squared increments between observations not exceeding a suitable threshold function. We also reconstruct the drift and the jump intensity coefficients when they are level-dependent and jumps have finite activity, through consistent and asymptotically normal estimators. Simulated experiments show that the newly proposed estimators perform better in finite samples than alternative estimators, and this allows us to reexamine the estimation of a univariate model for the short term interest rate, for which we find fewer jumps and more variance due to the diffusion part than previous studies.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 160 (2011)
Issue (Month): 1 (January)
Pages: 77-92

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Handle: RePEc:eee:econom:v:160:y:2011:i:1:p:77-92

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Web page: http://www.elsevier.com/locate/jeconom

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Cited by:
  1. Fulvio Corsi & Davide Pirino & Roberto Renò, 2010. "Threshold bipower variation and the impact of jumps on volatility forecasting," Post-Print peer-00741630, HAL.
  2. Schmisser, Émeline, 2014. "Non-parametric adaptive estimation of the drift for a jump diffusion process," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 124(1), pages 883-914.
  3. Torben B. Rasmussen, 2009. "Jump Testing and the Speed of Market Adjustment," CREATES Research Papers 2009-08, School of Economics and Management, University of Aarhus.
  4. Cecilia Mancini & Vanessa Mattiussi & Roberto Reno', 2012. "Spot Volatility Estimation Using Delta Sequences," Working Papers - Mathematical Economics, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa 2012-10, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  5. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1174-1206, October.
  6. Rama Cont & Cecilia Mancini, 2010. "Nonparametric tests for pathwise properties of semimartingales," Working Papers - Mathematical Economics, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa 2010-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.

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