Estimation of Lévy Processes via Stochastic Programming and Kalman Filtering

Mark Anthony Caruana ()
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Mark Anthony Caruana: University of Malta

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 4, 1211-1225

Abstract: Abstract The estimation of Lévy process has received a lot of attention in recent years. Evidence of this is the extensive amount of literature concerning this problem which can be classified in two categories: the nonparametric approach, and the parametric approach. In this paper, we shall concentrate on the latter, and in particular the parameters will be estimated within a stochastic programming framework. To be more specific, the first derivative of the characteristic function and its empirical version shall be used in objective function. Furthermore, the parameter estimates are recursively estimated by making use of a modified extended Kalman filter (MEKF). Some properties of the parameter estimates are studied. Finally, a number of simulations will be carried out and the results are presented and discussed.

Keywords: Lévy processes; Kalman filter; Stochastic programming; Characteristic function; 60G51; 62F12 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11009-017-9552-9

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