Abstract Operator fractional Brownian motion (OFBM) is a multivariate extension of fractional Brownian motion and has operator self-similarity. The dependence structure across the components of OFBM is determined by the Hurst matrix H and E ( X H ( 1 ) X H ( 1 ) ′ ) . In this paper, the estimators of H with wavelet method is compared in continuous sample path and discrete sample path. It is proved that with a discrete sample path, the wavelet estimator has asymptotic bias that reveals the delicate dynamic within the Hurst parameters of H , scale parameter of wavelet function, and covariance structure of X H ( 1 ) . The scale parameter of wavelet function should be chosen differently to estimate Hurst parameters when Hurst index is greater than .5 than when it is less than .5 in discrete sample cases, whereas the largest scale parameter should be chosen regardless of the values of Hurst parameter when a continuous sample path is given.

中文翻译：

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OFBM中的小波估计：在不同的采样方法和不同的参数值中选择尺度参数

摘要 算子分数布朗运动(OFBM)是分数布朗运动的多元扩展，具有算子自相似性。OFBM 组件之间的依赖结构由 Hurst 矩阵 H 和 E (XH (1) XH (1)') 确定。本文在连续样本路径和离散样本路径下比较了小波法对H的估计。证明了在离散样本路径下，小波估计量具有渐近偏差，揭示了 H 的 Hurst 参数、小波函数的尺度参数和 XH ( 1 ) 的协方差结构内的微妙动态。在离散样本情况下，当 Hurst 指数大于 0.5 时和小于 0.5 时，应选择不同的小波函数尺度参数来估计 Hurst 参数，