Optimally thresholded realized power variations for Levy jump diffusion models

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Figueroa-Lopez, Jose E.¹  Nisen, Jeffrey¹ 

[1] Purdue Univ, Dept Stat, W Lafayette, IN 47907 USA

关键词: Volatility estimation;    Jump detection;    Levy processes;    Additive processes;    Nonparametric estimation;    Thresholded estimators;    Power variations;   

DOI  :  10.1016/j.spa.2013.04.006

来源: Elsevier

【 摘 要 】

Thresholded Realized Power Variations (TPVs) are one of the most popular nonparametric estimators for general continuous-time processes with a wide range of applications. In spite of their popularity, a common drawback lies in the necessity of choosing a suitable threshold for the estimator, an issue which so far has mostly been addressed by heuristic selection methods. To address this important issue, we propose an objective selection method based on desirable optimality properties of the estimators. Concretely, we develop a well-posed optimization problem which, for a fixed sample size and time horizon, selects a threshold that minimizes the expected total number of jump misclassifications committed by the thresholding mechanism associated with these estimators. We analytically solve the optimization problem under mild regularity conditions on the density of the underlying jump distribution, allowing us to provide an explicit infill asymptotic characterization of the resulting optimal thresholding sequence at a fixed time horizon. The leading term of the optimal threshold sequence is shown to be proportional to Levy's modulus of continuity of the underlying Brownian motion, hence theoretically justifying and sharpening selection methods previously proposed in the literature based on power functions or multiple testing procedures. Furthermore, building on the aforementioned asymptotic characterization, we develop an estimation algorithm, which allows for a feasible implementation of the newfound optimal sequence. Simulations demonstrate the improved finite sample performance offered by optimal TPV estimators in comparison to other popular non-optimal alternatives. (c) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free