ISSN 0253-2778

CN 34-1054/N

open
Free to Publish. Free to Read.
Open AccessOpen Access JUSTC Original Paper

Change-points estimation and model selection for piecewise stationary autoregressive processes based on modified adaptive LASSO method

  • International Institute of Finance, School of Management, University of Science and Technology of China, Hefei 230601, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.06.005
  • Received Date: 06 December 2019
  • Accepted Date: 20 April 2020
  • Rev Recd Date: 20 April 2020
  • Publish Date: 30 June 2020
    Abstract

  • Abstract

    Considering the problems of change-points estimation and model selection for nonstationary time series such as piecewise stationary autoregressive (PSAR) processes, a method which can simultaneously conduct change-point estimation and model selection with a two-stage LASSO (TS-LASSO) algorithm based on the existing method to transform the problem of change-points estimation into the problem of variable selection was proposed. Specifically, in the first stage, the preliminary estimation of change-points and the selection of the models can be derived by LASSO algorithm. Then, in the second stage, a modified adaptive LASSO algorithm was used to screen the overestimated results, so the consistent estimation could be obtained and the accurate model could be selected. The large sample properties of the results for the variable-point estimation. In addition, the TS-LASSO algorithm can also achieve the estimation and recognition for the mean change-points sequences and no change-points sequences in special cases effectively. Finally, combined with the test of different type of simulative sequences and the case study of a seismic wave data, it was shown that TS-LASSO algorithm is effective and has certain practicability.

    Abstract

    Considering the problems of change-points estimation and model selection for nonstationary time series such as piecewise stationary autoregressive (PSAR) processes, a method which can simultaneously conduct change-point estimation and model selection with a two-stage LASSO (TS-LASSO) algorithm based on the existing method to transform the problem of change-points estimation into the problem of variable selection was proposed. Specifically, in the first stage, the preliminary estimation of change-points and the selection of the models can be derived by LASSO algorithm. Then, in the second stage, a modified adaptive LASSO algorithm was used to screen the overestimated results, so the consistent estimation could be obtained and the accurate model could be selected. The large sample properties of the results for the variable-point estimation. In addition, the TS-LASSO algorithm can also achieve the estimation and recognition for the mean change-points sequences and no change-points sequences in special cases effectively. Finally, combined with the test of different type of simulative sequences and the case study of a seismic wave data, it was shown that TS-LASSO algorithm is effective and has certain practicability.
    • FullText(HTML)
  • loading
    • References(18)
  • [1]
    PAGE E S. Continuous inspection schemes [J]. Biometrika, 1954, 41:100-115.
    [2]
    PICARD D. Testing and estimating change-points in time series [J]. Advances in Applied Probability, 1985, 17(4):841-867.
    [3]
    TAKANAMI T, KITAGAWA G. A new efficient procedure for the estimation of onset times of seismic waves [J].Journal of Physics of the Earth, 1988, 36(6):267-290.
    [4]
    DAVISR A, LEE T C, RODRIGUEZYAM G A, et al. Structural break estimation for nonstationary time Series models[J].Journal of the American Statistical Association, 2006, 101(473): 223-239.
    [5]
    YAU C Y, ZHAO Z. Inference for multiple change points in time series via likelihood ratio scan statistics [J].Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2016, 78(4): 895-916.
    [6]
    吴楠,胡尧,王丹. 分段平稳时间序列中的多变点检测[J]. 理论数学, 2018,8(2):136-148.
    [7]
    HARCHAOUI Z, LVY-LEDUC C. Multiple change point estimation with a total variation penalty [J]. Journal of the American Statistical Association, 2010, 105(492): 1480-1493.
    [8]
    JIN B S, WU Y H, SHI X P. Consistent two-stage multiple change-point detection in linear models [J]. Canadian Journal of Statistics, 2016,44: 161-179.
    [9]
    CHAN N H, YAU C Y, ZHANG R M. Group LASSO for structural break time series [J]. Journal of the American Statistical Association, 2014, 109(506): 590-599.
    [10]
    王国长, 梁焙婷, 王金枝. 改进的自适应Lasso方法在股票市场中的应用 [J]. 数理统计与管理, 2019, 38(4): 750-760.
    [11]
    TIBSHIRANI R, SAUNDERS M, ROSSET S, et al. Sparsity and smoothness via the fused lasso [J]. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2005, 67: 91-108.
    [12]
    ZHAO P, YU B. On model selection consistency of Lasso [J].Journal of Machine Learning Research, 2006, 7: 2541-2563.
    [13]
    ZOU Hui. The adaptive Lasso and its oracle properties [J]. Journal of the American Statistical Association, 2006, 101(476): 1418-1429.
    [14]
    FAN J, LI R. Variable selection via non-concave penalized likelihood and its oracle properties [J]. Journal of the American statistical Association, 2001, 96(456): 1348-1360.
    [15]
    SHAO J. Linear model selection by cross validation [J]. Journal of the American Statistical Association, 1993, 88(422): 486-494.
    [16]
    何先龙, 佘天莉, 高峰. 一种地震P波和S波初至时间自动拾取的新方法[J]. 地球物理学报, 2016, 59(7): 2519-2527.
    [17]
    SHUMWAY R H, STOFFER D S. Time Series Analysis and Its Applications: With R examples [M]. Berlin: Springer, 2017.
    [18]
    CHAN N H. Time Series: Applications to Finance with R and S-Plus [M]. New York: Wiley, 2011.
    • Supplements(0)
    • Related Articles
    • Track Citations
  • 加载中

Catalog

    |
    Get Citation
    PDF
    XML
    [1]
    PAGE E S. Continuous inspection schemes [J]. Biometrika, 1954, 41:100-115.
    [2]
    PICARD D. Testing and estimating change-points in time series [J]. Advances in Applied Probability, 1985, 17(4):841-867.
    [3]
    TAKANAMI T, KITAGAWA G. A new efficient procedure for the estimation of onset times of seismic waves [J].Journal of Physics of the Earth, 1988, 36(6):267-290.
    [4]
    DAVISR A, LEE T C, RODRIGUEZYAM G A, et al. Structural break estimation for nonstationary time Series models[J].Journal of the American Statistical Association, 2006, 101(473): 223-239.
    [5]
    YAU C Y, ZHAO Z. Inference for multiple change points in time series via likelihood ratio scan statistics [J].Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2016, 78(4): 895-916.
    [6]
    吴楠,胡尧,王丹. 分段平稳时间序列中的多变点检测[J]. 理论数学, 2018,8(2):136-148.
    [7]
    HARCHAOUI Z, LVY-LEDUC C. Multiple change point estimation with a total variation penalty [J]. Journal of the American Statistical Association, 2010, 105(492): 1480-1493.
    [8]
    JIN B S, WU Y H, SHI X P. Consistent two-stage multiple change-point detection in linear models [J]. Canadian Journal of Statistics, 2016,44: 161-179.
    [9]
    CHAN N H, YAU C Y, ZHANG R M. Group LASSO for structural break time series [J]. Journal of the American Statistical Association, 2014, 109(506): 590-599.
    [10]
    王国长, 梁焙婷, 王金枝. 改进的自适应Lasso方法在股票市场中的应用 [J]. 数理统计与管理, 2019, 38(4): 750-760.
    [11]
    TIBSHIRANI R, SAUNDERS M, ROSSET S, et al. Sparsity and smoothness via the fused lasso [J]. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2005, 67: 91-108.
    [12]
    ZHAO P, YU B. On model selection consistency of Lasso [J].Journal of Machine Learning Research, 2006, 7: 2541-2563.
    [13]
    ZOU Hui. The adaptive Lasso and its oracle properties [J]. Journal of the American Statistical Association, 2006, 101(476): 1418-1429.
    [14]
    FAN J, LI R. Variable selection via non-concave penalized likelihood and its oracle properties [J]. Journal of the American statistical Association, 2001, 96(456): 1348-1360.
    [15]
    SHAO J. Linear model selection by cross validation [J]. Journal of the American Statistical Association, 1993, 88(422): 486-494.
    [16]
    何先龙, 佘天莉, 高峰. 一种地震P波和S波初至时间自动拾取的新方法[J]. 地球物理学报, 2016, 59(7): 2519-2527.
    [17]
    SHUMWAY R H, STOFFER D S. Time Series Analysis and Its Applications: With R examples [M]. Berlin: Springer, 2017.
    [18]
    CHAN N H. Time Series: Applications to Finance with R and S-Plus [M]. New York: Wiley, 2011.
    Recommended articles
    TrendMD
    Volume 50 Issue 6 page: 744-751
    Cover

    Article Metrics

    Article views (60) PDF downloads(121)
    Proportional views

    Copyright © Editorial Office of JUSTC, All Rights Reserved. 皖ICP备05002528号

    Supported by: Beijing Renhe Information Technology Co. Ltd    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return