José E. Figueroa-López, Cheng Li, Jeffrey Nisen
arXiv 19 Nov 2018 · Mathematics — Statistics Theory · publishedStatistical Inference for Stochastic Processes (2020) · 1 citations (OpenAlex)
arXiv:1811.07499 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we propose a new threshold-kernel jump-detection method for jump-diffusion processes, which iteratively applies thresholding and kernel methods in an approximately optimal way to achieve improved finite-sample performance. We use the expected number of jump misclassifications as the objective function to optimally select the threshold parameter of the jump detection scheme. We prove that the objective function is quasi-convex and obtain a new second-order infill approximation of the optimal threshold in closed form. The approximate optimal threshold depends not only on the spot volatility, but also the jump intensity and the value of the jump density at the origin. Estimation methods for these quantities are then developed, where the spot volatility is estimated by a kernel estimator with thresholding and the value of the jump density at the origin is estimated by a density kernel estimator applied to those increments deemed to contain jumps by the chosen thresholding criterion. Due to the interdependency between the model parameters and the approximate optimal estimators built to estimate them, a type of iterative fixed-point algorithm is developed to implement them. Simulation studies for a prototypical stochastic volatility model show that it is not only feasible to implement the higher-order local optimal threshold scheme but also that this is superior to those based only on the first order approximation and/or on average values of the parameters over the estimation time period.
appendix boundary found by appendix_command · 61% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | J.E. Figueroa-López and J. Nisen (2013) Optimally thresholded realized power variations for Lévy jump diffusion models | 1.000 | 11 | 5 | 100% |
| 2 | J.E. Figueroa-López and J. Nisen (2019) Second-order properties of thresholded realized power variations of FJA additive processes | 0.811 | 4 | 2 | 100% |
| 3 | J.E. Figueroa-López and C. Li (2020) Optimal kernel estimation of spot volatility of stochastic differential equations | 0.693 | 14 | 1 | 100% |
| 4 | J.E. Figueroa-López and C. Mancini (2019) Optimum thresholding using mean and conditional mean square error | 0.644 | 2 | 2 | 100% |
| 5 | C. Mancini (2009) Non parametric threshold estimation for models with stochastic diffusion coefficient and jumps | 0.644 | 2 | 2 | 100% |
| 6 | L. Zhang, P. Mykland, and Y. Aẗ-Sahalia (2005) A tale of two time scales | 0.644 | 2 | 2 | 100% |
| 7 | J. Fan and Y. Wang (2008) Spot volatility estimation for high-frequency data | 0.644 | 2 | 2 | 100% |
| 8 | D. Foster and D. Nelson (1996) Continuous record asymptotics for rolling sample variance estimators | 0.644 | 2 | 2 | 100% |
| 9 | Y. Aït-Sahalia and J. Jacod (2014) High-Frequency Financial Econometrics | 0.511 | 2 | 1 | 100% |
| 10 | D. Kristensen (2010) Nonparametric filtering of the realized spot volatility: A kernel-based approach | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 26 scored citations.