A Least Squares Estimator for Lévy-driven Moving Averages Based on Discrete Time Observations

Shibin Zhang, Zhengyan Lin and Xinsheng Zhang

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 6, 1111-1129

Abstract: This article is concerned with a least squares estimator (LSE) of the kernel function parameter θ for a Lévy-driven moving average of the form X(t) = ∫t− ∞K(θ(t − s)) dL(s), where L={L(t),t∈R}$L=\lbrace L(t),t\in \mathbb {R}\rbrace$ is a Lévy process without the Brownian motion part, K is a kernel function and θ > 0 is a parameter. Let h be the time span between two consecutive observations and let n be the size of sample. As h → 0 and nh → ∞, consistency and asymptotic normality of the LSE are studied. The small-sample performance of the LSE is evaluated by means of a simulation experiment. Finally, two real-data applications show that the Lévy-driven moving average gives a good approximation to the autocorrelation of the process.

Date: 2015
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DOI: 10.1080/03610926.2012.763093

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