2014/10/23 by Vicky Fasen, Fasen, Vicky
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F05 #60G10 #62F12 #62M10 #Advanced Statistical Process Monitoring #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability and Risk Models #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1410.6273
openalex publication_date 2014/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper considers high frequency sampled multivariate continuous-time ARMA\n(MCARMA) models, and derives the asymptotic behavior of the sample\nautocovariance function to a normal random matrix. Moreover, we obtain the\nasymptotic behavior of the cross-covariances between different components of\nthe model. We will see that the limit distribution of the sample autocovariance\nfunction has a similar structure in the continuous-time and in the\ndiscrete-time model. As special case we consider a CARMA (one-dimensional\nMCARMA) process. For a CARMA process we prove Bartlett's formula for the sample\nautocorrelation function. Bartlett's formula has the same form in both models,\nonly the sums in the discrete-time model are exchanged by integrals in the\ncontinuous-time model. Finally, we present limit results for multivariate MA\nprocesses as well which are not known in this generality in the multivariate\nsetting yet.\n