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基于二次平滑-灰色预测的在线投资组合选择

刘晓玉 黄定江

刘晓玉, 黄定江. 基于二次平滑-灰色预测的在线投资组合选择[J]. 华东师范大学学报(自然科学版), 2020, (6): 115-128. doi: 10.3969/j.issn.1000-5641.201921020
引用本文: 刘晓玉, 黄定江. 基于二次平滑-灰色预测的在线投资组合选择[J]. 华东师范大学学报(自然科学版), 2020, (6): 115-128. doi: 10.3969/j.issn.1000-5641.201921020
LIU Xiaoyu, HUANG Dingjiang. Online portfolio selection based on quadratic smooth-gray prediction[J]. Journal of East China Normal University (Natural Sciences), 2020, (6): 115-128. doi: 10.3969/j.issn.1000-5641.201921020
Citation: LIU Xiaoyu, HUANG Dingjiang. Online portfolio selection based on quadratic smooth-gray prediction[J]. Journal of East China Normal University (Natural Sciences), 2020, (6): 115-128. doi: 10.3969/j.issn.1000-5641.201921020

基于二次平滑-灰色预测的在线投资组合选择

doi: 10.3969/j.issn.1000-5641.201921020
基金项目: 国家自然科学基金(11501204, U1711262)
详细信息
    通讯作者:

    黄定江, 男, 研究员, 博士生导师, 研究领域为机器学习与人工智能. E-mail: djhuang@dase.ecnu.edu.cn

  • 中图分类号: TP399

Online portfolio selection based on quadratic smooth-gray prediction

  • 摘要: 在线投资组合是近年来计算金融领域热门的研究课题. 目前已有的策略, 对股票价格的预测效果并不十分理想, 而对股价的准确预测对投资组合方式有重要的指导意义. 考虑到股价的滞后性及其分布的复杂性, 首次利用股价中的二阶信息, 提出了DMAR (DMA (Double Moving Average) Reversion)、DEAR (DEA (Double Exponential Average) Reversion)、GMR (GM Reversion)、DA-GMR (DA-GM Reversion) 4种投资组合策略: 分别通过二次移动平均法、二次指数滑动预测法、灰色预测法, 对下一期的价格数据进行了预测、集成学习; 将二次平滑预测和灰色预测的结果进行了优化, 得到了下一期的预测价格; 再利用被动攻击(Passive-Aggressive, PA)算法更新投资组合, 最终得到了4种投资组合策略, 并在真实的金融市场的数据集中验证了策略的有效性. 结果表明, 与已有的算法相比, 在NYSE (O)、NYSE (N)、DJIA和MSCI 这4个真实的金融市场的数据集上, 所提出的4种投资组合策略都达到了较高的累计收益.
  • 图  1  策略DMAR的累计收益在DJIA数据集上关于交易费用比的分析

    Fig.  1  Analysis of the cumulative income of strategy DMAR with respect to transaction cost ratio on DJIA

    表  1  4个来源于真实市场的实验数据集

    Tab.  1  Four experimental datasets from the real market

    数据集区域时间范围周期/天资产/个
    NYSE(O) 美国 1962-07-03—1984-12-31 5 651 36
    NYSE(N) 美国 1985-01-01—2010-06-30 6 431 23
    DJIA 美国 2001-01-01—2003-01-14 507 30
    MSCI 24个国家及地区 2006-04-01—2010-03-31 1 043 24
    下载: 导出CSV

    表  2  策略在4个真实数据集上的累计收益

    Tab.  2  The cumulative benefit of the strategy on four real datasets

    方法数据集
    NYSE(O)NYSE(N)DJIAMSCI
    Market 14.50 18.06 0.76 0.91
    Best-stock 54.14 83.51 1.19 1.50
    BCRP 250.60 120.32 1.24 1.51
    UP 26.68 31.49 0.81 0.92
    EG 27.09 31.00 0.81 0.93
    ONS 109.91 21.59 1.53 0.86
    Bk 1.08E+09 4.64E+03 0.68 2.64
    BNN 3.35E+11 6.80E+04 0.88 13.47
    CORN 1.48E+13 5.37E+05 0.84 26.19
    Anticor 2.41E+08 6.21E+06 2.29 3.22
    PAMR 5.14E+15 1.25E+06 0.68 15.23
    CWMR 6.49E+15 1.41E+06 0.68 17.28
    OLMAR 3.68E+16 2.54E+08 2.12 16.39
    RMR 2.07E+17 2.70E+08 2.58 16.36
    DMAR 4.03e+16 2.25E+08 2.09 16.54
    DEAR 1.98E+18 4.67E+08 2.21 19.16
    GMR 2.43E+17 4.86E+08 2.33 15.31
    DA-GMR 1.45E+18 1.30E+08 1.91 24.18
    注: 黑色粗体表示相应数据集中的最优实验结果
    下载: 导出CSV

    表  3  DMAR策略的各项统计检验指标

    Tab.  3  Statistical test indicators for the DEAR strategy

    统计检验指标数据集
    NYSE(O)NYSE(N)DJIAMSCI
    Size 5 651 6 431 507 1 043
    MER(DMAR) 0.000 5 0.003 6 0.002 0 0.003 0
    MER(Market) 0.000 5 0.000 5 –0.000 4 0.000 0
    WR 0.568 9 0.531 8 0.526 6 0.585 8
    alpha 0.006 8 0.003 0 0.002 6 0.003 0
    beta 1.299 8 1.179 0 1.254 2 1.179 4
    t 统计量 15.225 2 7.350 0 2.155 4 5.847 5
    p 0.000 0 0.000 0 0.015 8 0.000 0
    下载: 导出CSV

    表  4  DEAR策略的各项统计检验指标

    Tab.  4  Statistical test indicators for the DEAR strategy

    统计检验指标数据集
    NYSE(O)NYSE(N)DJIAMSCI
    Size 5 651 6 431 507 1 043
    MER(DEAR) 0.008 1 0.003 8 0.002 6 0.003 1
    MER(Market) 0.000 5 0.000 5 –0.000 4 0.000 0
    WR 0.580 8 0.541 0 0.564 1 0.598 3
    alpha 0.007 41 0.003 3 0.003 1 0.003 1
    beta 1.297 2 1.136 9 1.190 9 1.190 1
    t 统计量 17.420 8 7.853 2 2.728 3 6.511 7
    p 0.000 0 0.000 0 0.000 0 0.000 0
    下载: 导出CSV

    表  5  GMR 策略的各项统计检验指标

    Tab.  5  Statistical test indicators for the GMR strategy

    统计检验指标数据集
    NYSE(O)NYSE(N)DJIAMSCI
    Size 5 651 6 431 507 1 043
    MER(GMR) 0.007 7 0.003 8 0.002 2 0.002 9
    MER(Market) 0.000 5 0.000 5 –0.000 4 0.000 0
    WR 0.571 2 0.538 8 0.548 3 0.584 9
    alpha 0.007 1 0.003 2 0.002 8 0.002 9
    beta 1.326 8 1.145 8 1.250 5 1.206 0
    t 统计量 5.594 0 7.548 8 2.311 2 5.594 0
    p 0.000 0 0.000 0 0.000 0 0.000 0
    下载: 导出CSV

    表  6  DA-GMR 策略的各项统计检验指标

    Tab.  6  Statistical test indicators for the DA-GMR strategy

    统计检验指标数据集
    NYSE(O)NYSE(N)DJIAMSCI
    Size 5 651 6 431 507 1 043
    MER(DA-GMR) 0.007 9 0.003 4 0.001 8 0.003 3
    MER(Market) 0.000 5 0.000 5 –0.000 4 0.000 0
    WR 0.583 4 0.540 7 0.544 4 0.610 7
    alpha 0.007 3 0.002 9 0.002 3 0.003 3
    beta 1.286 5 1.115 8 1.291 2 1.180 2
    t 统计量 18.077 0 7.581 5 2.201 0 7.299 1
    p 0.000 0 0.000 0 0.000 0 0.000 0
    下载: 导出CSV

    表  7  策略间5个性能指标的比较

    Tab.  7  Comparison of five performance indicators between strategies

    性能指标策略数据集
    NYSE(O)NYSE(N)DJIAMSCI
    OLMAR 4.662 6 1.105 1 0.434 6 1.012 1
    RMR 5.125 1 1.110 0 0.605 8 1.011 2
    DMAR 4.685 8 1.095 5 0.446 5 1.016 6
    APY DEAR 5.787 7 1.155 1 0.485 7 1.092 2
    GMR 5.170 4 1.158 4 0.524 8 0.978 2
    DA-GMR 5.691 2 1.051 3 0.380 9 1.217 5
    OLMAR 0.565 7 0.568 4 0.521 6 0.391 3
    RMR 0.569 9 0.566 7 0.516 4 0.392 9
    DMAR 0.565 3 0.568 0 0.522 0 0.391 2
    Volatility DEAR 0.544 0 0.550 5 0.503 9 0.382 3
    GMR 0.571 2 0.577 2 0.525 4 0.400 6
    DA-GMR 0.520 0 0.524 4 0.492 4 0.372 9
    OLMAR 8.170 8 1.873 9 0.756 5 2.484 6
    RMR 8.923 5 1.888 0 1.095 7 2.472 1
    DMAR 8.218 9 1.858 2 0.778 6 2.496 1
    SR DEAR 10.564 8 2.025 6 0.884 6 2.752 2
    GMR 8.982 3 1.937 7 0.922 8 2.341 7
    DA-GMR 10.868 6 1.928 5 0.692 4 3.157 7
    OLMAR 0.436 2 0.933 4 0.439 5 0.453 7
    RMR 0.424 8 0.905 2 0.370 5 0.508 5
    DMAR 0.435 6 0.935 9 0.447 7 0.452 9
    MDD DEAR 0.354 6 0.920 0 0.388 4 0.414 3
    GMR 0.437 8 0.927 2 0.311 5 0.467 0
    DA-GMR 0.344 8 0.849 1 0.505 3 0.401 9
    OLMAR 10.689 8 1.184 0 0.988 9 2.230 6
    RMR 12.063 3 1.226 2 1.634 9 1.988 7
    DMAR 10.758 2 1.170 5 0.997 2 2.244 4
    CR DEAR 16.321 1 1.2555 1.250 7 2.636 3
    GMR 11.809 5 1.249 3 1.685 0 2.094 7
    DA-GMR 16.505 3 1.238 1 0.753 8 3.029 1
    注: 黑色粗体表示相应数据集中的最优实验结果
    下载: 导出CSV
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  • 收稿日期:  2019-08-27
  • 刊出日期:  2020-11-25

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