 Nonparametric inference for the spectral measure of a bivariate pure-jump semimartingaleViktor Todorov Stochastic Processes and their Applications, 2019, vol. 129, issue 2, 419-451 Abstract: We develop a nonparametric estimator for the spectral density of a bivariate pure-jump Itô semimartingale from high-frequency observations of the process on a fixed time interval with asymptotically shrinking mesh of the observation grid. The process of interest is locally stable, i.e., its Lévy measure around zero is like that of a time-changed stable process. The spectral density function captures the dependence between the small jumps of the process and is time invariant. The estimation is based on the fact that the characteristic exponent of the high-frequency increments, up to a time-varying scale, is approximately a convolution of the spectral density and a known function depending on the jump activity. We solve the deconvolution problem in Fourier transform using the empirical characteristic function of locally studentized high-frequency increments and a jump activity estimator. Keywords: Deconvolution; Fourier transform; High-frequency data; Itô semimartingale; Nonparametric inference; Spectral density (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:2:p:419-451 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2018.03.006 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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