分数布朗运动导数的弱收敛性

IF 1 4区经济学 Q3 ECONOMICS

Econometric Theory Pub Date : 2022-08-04 DOI:10.1017/s0266466622000639

S. Johansen, M. Nielsen

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引用次数: 0

摘要

众所周知，在适当的正则性条件下，对于$d>\frac｛1｝｛2｝$，具有分数参数d的归一化分数过程弱收敛于分数布朗运动（fBm）。我们证明，对于任何非负整数M，归一化分式过程的阶导数$M=0，1，\dots，M$相对于分式参数d联合弱收敛于fBm的相应导数。举例来说，我们将结果应用于多分数向量自回归模型中得分向量的渐近分布。

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WEAK CONVERGENCE TO DERIVATIVES OF FRACTIONAL BROWNIAN MOTION

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.

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来源期刊

Econometric Theory MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Since its inception, Econometric Theory has aimed to endow econometrics with an innovative journal dedicated to advance theoretical research in econometrics. It provides a centralized professional outlet for original theoretical contributions in all of the major areas of econometrics, and all fields of research in econometric theory fall within the scope of ET. In addition, ET fosters the multidisciplinary features of econometrics that extend beyond economics. Particularly welcome are articles that promote original econometric research in relation to mathematical finance, stochastic processes, statistics, and probability theory, as well as computationally intensive areas of economics such as modern industrial organization and dynamic macroeconomics.