Two-step estimation of ergodic Lévy driven SDE

2015/05/08 by H. Masuda, Masuda, Hiroki, Yuma Uehara +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1505.01922

openalex publication_date 2015/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider high frequency samples from ergodic Lévy driven stochastic differential equation (SDE) with drift coefficient a(x,α) and scale coefficient c(x,γ) involving unknown parameters α and γ. We suppose that the Lévy measure ν₀, has all order moments but is not fully specified. We will prove the joint asymptotic normality of some estimators of α, γ and a class of functional parameter ∫φ(z)ν₀(dz), which are constructed in a two-step manner: first, we use the Gaussian quasi-likelihood for estimation of (α,γ), and then, for estimating ∫φ(z)ν₀(dz) we makes use of the method of moments based on the Euler-type residual with the the previously obtained quasi-likelihood estimator.

Citations

• Statistics of Random Processes

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