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Statistical inference of spectral estimation for continuous-time MA processes with finite second moments

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Abstract

In this paper we investigate a continuous-time MA (moving average) process (X t ) t≥0 sampled at an equally spaced time grid {Δ,2Δ, …, nΔ}, where the grid distance Δ > 0 is fixed and n denotes the number of observations, in the frequency domain. We derive for the process (X kΔ) k∈ℕ with finite second moments the asymptotic behavior of the periodogram and of the lag-window spectral density estimator. The periodogram is not a consistent estimator for the spectral density of (X kΔ) k∈ℕ. Different periodogram frequencies are asymptotically independent and exponentially distributed like for ARMA processes in discrete time. This result is basic for frequency bootstraps. In contrast, the lag-window spectral density estimator is a consistent estimator for the spectral density of (X kΔ) k∈ℕ and moreover, it is asymptotically normally distributed.

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  1. Inst. of Stochastics, Karlsruhe Inst. of Technology, Karlsruhe, Germany

    V. Fasen

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Fasen, V. Statistical inference of spectral estimation for continuous-time MA processes with finite second moments. Math. Meth. Stat. 22, 283–309 (2013). https://doi.org/10.3103/S1066530713040029

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  • DOI: https://doi.org/10.3103/S1066530713040029

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