Dependence Estimation for High‐frequency Sampled Multivariate CARMA Models |
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Authors: | Vicky Fasen |
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Institution: | Institute of Stochastics, Karlsruhe Institute of Technology, Karlsruhe, Germany |
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Abstract: | The paper considers high‐frequency sampled multivariate continuous‐time autoregressive moving average (MCARMA) models and derives the asymptotic behaviour of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behaviour of the cross‐covariances 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 a 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 discrete‐time 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. |
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Keywords: | asymptotic normality Bartlett's formula CARMA process consistency correlation function covariance function high‐frequency data Lé vy process limit theorems MA process multivariate models VARMA process |
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