基于极大重叠离散小波变换的金融高频数据波动率估计

吉林大学学报(理学版)

基于极大重叠离散小波变换的金融高频数据波动率估计

秦喜文^1,2, 刘文博³, 董小刚¹, 王纯杰¹, 李纯净^1

1. 长春工业大学基础科学学院, 长春 130012； 2. 吉林大学数学学院, 长春 130012；3. 吉林建筑大学基础科学部, 长春 130118

收稿日期:2014-03-10 出版日期:2014-11-26 发布日期:2014-12-11
通讯作者: 董小刚 E-mail:dongxiaogang@mail.ccut.edu.cn

Volatility Estimation of Financial High Frequency Data Based on Maximum Overlap Discrete Wavelet Transform

QIN Xiwen^1,2, LIU Wenbo^3, DONG Xiaogang^1, WANG Chunjie^1, LI Chunjing^1

1. School of Basic Science, Changchun University of Technology, Changchun 130012, China;2. College of Mathematics, Jilin University, Changchun 130012, China;3. Department of Basic Science, Jilin Jianzhu University, Changchun 130118, China

Received:2014-03-10 Online:2014-11-26 Published:2014-12-11
Contact: DONG Xiaogang E-mail:dongxiaogang@mail.ccut.edu.cn

摘要/Abstract

摘要：

利用极大重叠离散小波变换方法对资产收益的积分波动率进行估计. 针对沪深300指数选取不同小波函数估计积分波动率, 计算相对误差统计量. 结果表明, 不同小波函数对积分波动率估计不存在显著差异, 但随着抽样频率的增加, 估计精度逐渐提高. 对尺度及其相应尺度下的波动率进行对数变换可见, 二者之间存在显著的线性关系, 随着尺度的增加, 波动率逐渐变小.

关键词: 高频数据, 极大重叠离散小波变换, 波动率估计, 小波方差

Abstract:

Integrated volatility of asset return was estimated by means of maximum overlap discrete wavelet transform. The different wavelet functions were chosen to estimate the integrated volatility of Shanghai and Shenzhen 300 indices, and relative error statistics was calculated. The results show that integrated volatilities based on different wavelets had no significant difference. The estimated accuracy was improved with the increasing of sampling frequency. There was an obvious linear relationship between logarithmic scale and logarithmic volatility. The volatility decreasd gradually with the scale increasing.

Key words: high frequency data, maximum overlap discrete wavelet, volatility estimation, wavelet variance

中图分类号:

秦喜文, 刘文博, 董小刚, 王纯杰, 李纯净. 基于极大重叠离散小波变换的金融高频数据波动率估计[J]. 吉林大学学报(理学版), 2014, 52(06): 1222-1226.

QIN Xiwen, LIU Wenbo, DONG Xiaogang, WANG Chunjie, LI Chunjing. Volatility Estimation of Financial High Frequency Data Based on Maximum Overlap Discrete Wavelet Transform[J]. Journal of Jilin University Science Edition, 2014, 52(06): 1222-1226.

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