Dependence Estimation for High-frequency Sampled Multivariate CARMA Models
| Autor: | Vicky Fasen |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Multivariate statistics Covariance function 05 social sciences Asymptotic distribution Correlation function (astronomy) 01 natural sciences Lévy process 010104 statistics & probability Autocovariance 0502 economics and business Statistics Statistics::Methodology Applied mathematics Limit (mathematics) 0101 mathematics Statistics Probability and Uncertainty Random matrix 050205 econometrics Mathematics |
| Zdroj: | Scandinavian Journal of Statistics. 43:292-320 |
| ISSN: | 0303-6898 |
| DOI: | 10.1111/sjos.12180 |
| Popis: | The paper considers high frequency sampled multivariate continuous-time ARMA (MCARMA) models, and derives the asymptotic behavior of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behavior of the crosscovariances between different components of the model. We will see that the limit distribution of the sample autocovariance function has a similar structure in the continuous-time and in the discrete-time model. As special case we consider a CARMA (one-dimensional MCARMA) process. For a CARMA process we prove Bartlett’s formula for the sample autocorrelation function. Bartlett’s formula has the same form in both models, only the sums in the discretetime model are exchanged by integrals in the continuous-time model. Finally, we present limit results for multivariate MA processes as well which are not known in this generality in the multivariate setting yet. |
| Databáze: | OpenAIRE |
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