WEAK CONVERGENCE TO DERIVATIVES OF FRACTIONAL BROWNIAN MOTION
| Autor: | Søren Johansen, Morten Ørregaard Nielsen |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Johansen, S & Nielsen, M Ø 2022, ' Weak convergence to derivatives of fractional Brownian motion ', Econometric Theory . https://doi.org/10.1017/S0266466622000639 Johansen, S & Nielsen, M Ø 2023, ' WEAK CONVERGENCE TO DERIVATIVES OF FRACTIONAL BROWNIAN MOTION ', Econometric Theory, pp. 1-16 . https://doi.org/10.1017/S0266466622000639 |
| ISSN: | 1469-4360 0266-4666 |
| DOI: | 10.1017/s0266466622000639 |
| Popis: | It is well known that, under suitable regularity conditions, the normalized fractional process with fractional parameter d converges weakly to fractional Brownian motion (fBm) for $d>\frac {1}{2}$ . We show that, for any nonnegative integer M, derivatives of order $m=0,1,\dots ,M$ of the normalized fractional process with respect to the fractional parameter d jointly converge weakly to the corresponding derivatives of fBm. As an illustration, we apply the results to the asymptotic distribution of the score vectors in the multifractional vector autoregressive model. |
| Databáze: | OpenAIRE |
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