华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (5): 76-84.

• 应用数学 • 上一篇    下一篇

局部自相似过程的小波估计

陆智萍1, 陶勤英2   

  1. 1. 华东师范大学~~国际金融与风险管理研究中心, 上海 200241; 2. 华东师范大学~~数学系, 上海 200241
  • 收稿日期:2011-12-01 修回日期:2012-03-01 出版日期:2012-09-25 发布日期:2012-09-29

Wavelet estimation for locally self-similar processes

LU Zhi-ping 1, TAO Qin-ying 2   

  1. 1. Research Center of International Finance and Risk Management, East China Normal University, Shanghai 200241, China; 2. Department of Mathematics, East China Normal University, Shanghai 200241, China
  • Received:2011-12-01 Revised:2012-03-01 Online:2012-09-25 Published:2012-09-29

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摘要： 首先, 针对时变自相似参数提出了一种基于最大重叠离散小波变换的估计方法; 对此进行了蒙特卡洛模拟研究, 发现提高了估计的精度; 最后, 将研究结果应用于海洋垂直切变序列.

关键词: 局部自相似过程, 长记忆, 蒙特卡洛模拟, 最小二乘法回归, 小波变换

Abstract: A new estimation method was proposed based on the maximal overlap discrete wavelet transform, which provided a good alternative for the estimation of the time-varying self-similarity parameters. It also included a simulation-based study using Monte Carlo method, which increases the accuracy of the estimation. Finally, an application was made on the vertical ocean shear measurements.

Key words: locally self-similar process, long memory, Monte Carlo simulation, OLS regression, wavelet transform

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