Asymptotic moving average representation of high-frequency sampled multivariate CARMA processes
| Autor: | Péter Kevei |
|---|---|
| Přispěvatelé: | Lehrstuhl für Mathematische Statistik |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Discrete mathematics Multivariate statistics 010102 general mathematics Univariate Spectral density 01 natural sciences Moving-average model ddc 010104 statistics & probability Moving average Statistics Autoregressive–moving-average model Multivariate continuous time autoregressive moving average (CARMA) process Spectral density High-frequency sampling Discretely sampled process 0101 mathematics Asymptotic expansion Representation (mathematics) Mathematics |
| Zdroj: | Annals of the Institute of Statistical Mathematics. 70:467-487 |
| ISSN: | 1572-9052 0020-3157 |
| DOI: | 10.1007/s10463-017-0601-5 |
| Popis: | High-frequency sampled multivariate continuous time autoregressive moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process $$(Y_{n\varDelta })_{n \in {\mathbb {Z}}}$$ as $$\varDelta \downarrow 0$$ , where $$(Y_t)_{t \in {\mathbb {R}}}$$ is an MCARMA process. We show that the properly filtered process is a vector moving average process, and determine the asymptotic moving average representation of it, thus generalizing the univariate results to the multivariate model. The determination of the moving average representation of the filtered process, important for the analysis of high-frequency data, is difficult for any fixed positive $$\varDelta $$ . However, the results established here provide a useful and insightful approximation when $$\varDelta $$ is very small. |
| Databáze: | OpenAIRE |
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