Weak convergence of multivariate fractional processes. (English) Zbl 1028.60030
For a wide class of nonstationary fractionally integrated multivariate processes, weak convergence to the vector fractional Brownian motion of the form \(W(r;\Omega) = \int _0^r G(r,s) dB(r,\Omega)\) is proved where \(G\) is a suitable matrix kernel and \(B(r,\Omega)\) denotes a Brownian motion with the incremental covariance matrix \(\Omega \). A functional central limit theorem is also established.
Reviewer: Bohdan Maslowski (Praha)
MSC:
| 60F17 | Functional limit theorems; invariance principles |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
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