Research article

Wild multiplicative bootstrap for M and GMM estimators in time series

  • Received: 03 January 2019 Accepted: 01 April 2019 Published: 08 April 2019
  • JEL Codes: C12, C13, C15

  • We introduce a wild multiplicative bootstrap for M and GMM estimators in nonlinear models when autocorrelation structures of moment functions are unknown. The implementation of the bootstrap algorithm does not require any parametric assumptions on the data generating process. After proving its validity, we also investigate the accuracy of our procedure through Monte Carlo simulations. The wild bootstrap algorithm always outperforms inference based on standard first-order asymptotic theory. Moreover, in most cases the accuracy of our procedure is also better and more stable than that of block bootstrap methods. Finally, we apply the wild bootstrap approach to study the forecast ability of variance risk premia to predict future stock returns. We consider US equity from 1990 to 2010. For the period under investigation, our procedure provides significance in favor of predictability. By contrast, the block bootstrap implies ambiguous conclusions that heavily depend on the selection of the block size.

    Citation: Francesco Audrino, Lorenzo Camponovo, Constantin Roth. Wild multiplicative bootstrap for M and GMM estimators in time series[J]. Quantitative Finance and Economics, 2019, 3(1): 165-186. doi: 10.3934/QFE.2019.1.165

    Related Papers:

  • We introduce a wild multiplicative bootstrap for M and GMM estimators in nonlinear models when autocorrelation structures of moment functions are unknown. The implementation of the bootstrap algorithm does not require any parametric assumptions on the data generating process. After proving its validity, we also investigate the accuracy of our procedure through Monte Carlo simulations. The wild bootstrap algorithm always outperforms inference based on standard first-order asymptotic theory. Moreover, in most cases the accuracy of our procedure is also better and more stable than that of block bootstrap methods. Finally, we apply the wild bootstrap approach to study the forecast ability of variance risk premia to predict future stock returns. We consider US equity from 1990 to 2010. For the period under investigation, our procedure provides significance in favor of predictability. By contrast, the block bootstrap implies ambiguous conclusions that heavily depend on the selection of the block size.


    加载中


    [1] Allen J, Gregory AW, Shimotsu K (2011) Empirical likelihood block bootstrapping. J Econom 161: 110-121. doi: 10.1016/j.jeconom.2010.10.003
    [2] Altonji JG, Segal LM (1996) Small-sample bias in GMM estimation of covariance structures. J Bus Econ Stat 14: 353-366.
    [3] Andrews DWK(1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59: 817-858.
    [4] Andrews DWK (2002) Higher-order improvements of a computationally attractive k-step bootstrap for extremum estimators. Econometrica 70: 119-162. doi: 10.1111/1468-0262.00271
    [5] Bollerslev T, Tauchen G, Zhou H (2009) Expected stock returns and variance risk premia. Rev Financ Stud 22: 4463-4492. doi: 10.1093/rfs/hhp008
    [6] Bücher A, Kojadinovic I (2016) A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing. Bernoulli 22: 927-968. doi: 10.3150/14-BEJ682
    [7] Campbell JY, Shiller RJ (1988) The dividend ratio model and small sample bias: a Monte Carlo study. Econ Lett 29: 325-331.
    [8] Campbell JY, Yogo M (2006) Efficient tests of stock return predictability. J Financ Econ 81: 27-60. doi: 10.1016/j.jfineco.2005.05.008
    [9] Camponovo L, Scaillet O, Trojani F (2012) Robust subsampling. J Econom 167: 197-210. doi: 10.1016/j.jeconom.2011.11.005
    [10] Camponovo L, Scaillet O, Trojani F (2015) Predictability hidden by anomalous observations. Working paper.
    [11] Carlstein E (1986) The use of subseries methods for estimating the variance of a general statistic from a stationary time series. Ann Stat 14: 1171-1179. doi: 10.1214/aos/1176350057
    [12] Chernozhukov V, Chetverikov D, Kato K (2014) Central limit theorems and multiplier bootstrap when p is much larger than n. Ann Stat, In press.
    [13] Davidson J (1994) Stochastic Limit Theory, Oxford University Press, Oxford.
    [14] De Jong RM, Davidson J (2000) Consistency of kernel estimators of heteroscedastic and autocorrelated covariance matrices. Econometrica 68: 407-424. doi: 10.1111/1468-0262.00115
    [15] Fama E, French K (1988) Dividend yields and expected stock returns. J Financ Econ 22: 3-25. doi: 10.1016/0304-405X(88)90020-7
    [16] Geyer C (1994) On the asymptotics of constrained M-estimation. Ann Stat 22: 1993-2010. doi: 10.1214/aos/1176325768
    [17] Goncalves S, White H (2004) Maximum likelihood and the bootstrap for nonlinear dynamic models. J Econom 119: 199-219. doi: 10.1016/S0304-4076(03)00204-5
    [18] Götze F, Künsch HR (1996) Second-order correctness of the blockwise bootstrap for stationary observations. Ann Stat 24: 1914-1933. doi: 10.1214/aos/1069362303
    [19] Hall P (1985) Resampling a coverage process. Stoch Process Their Appl 19: 259-269. doi: 10.1016/0304-4149(85)90028-6
    [20] Hall AR (2005) Generalized Method of Moments, Oxford University Press, Oxford.
    [21] Hall P, Horowitz J (1996) Bootstrap critical values for tests based on Generalized- Method-of-Moment estimators. Econometrica 64: 891-916. doi: 10.2307/2171849
    [22] Hall P, Horowitz JL, Jing BY (1995) On blocking rules for the bootstrap with dependent data. Biometrika 82: 561-574. doi: 10.1093/biomet/82.3.561
    [23] Hansen LP (1982) Large sample properties of generalized method of moments estimators. Econometrica 50: 1029-1054. doi: 10.2307/1912775
    [24] Huber PJ (1964) Robust estimation of a location parameter. Ann Math Stat 35: 73-101. doi: 10.1214/aoms/1177703732
    [25] Politis DN, Romano JP (1992) A general resampling scheme for triangular arrays of α-mixing random variables with application to the problem of spectral density estimation. Ann Stat 20: 1985-2007. doi: 10.1214/aos/1176348899
    [26] Politis DN, Romano JP (1992) The stationary bootstrap. J Am Stat Assoc 89: 1303-1313.
    [27] Inoue A, Shintani M (2006) Bootstrapping GMM estimators for time series. J Econom 133: 531-555. doi: 10.1016/j.jeconom.2005.06.004
    [28] Kline P, Santos A (2012) A score based approach to wild bootstrap inference. J Econom Method 1: 23-41.
    [29] Künsch H (1989) The jacknife and the bootstrap for general stationary observations. Ann Stat 17: 1217-1241. doi: 10.1214/aos/1176347265
    [30] Jansson M, Moreira MJ (2006) Optimal inference in regression models with nearly integrated regressors. Econometrica 74: 681-714. doi: 10.1111/j.1468-0262.2006.00679.x
    [31] Lahiri S (1996) Edgeworth expansion and moving block bootstrap for studentized M-estimators in multiple linear regression models. J Multivar Anal 56: 42-59. doi: 10.1006/jmva.1996.0003
    [32] Lazarus E, Lewis DJ, Stock JH, et al. (2018) HAR inference: recommendations for practice rejoinder. J Bus Econ Stat 36: 541-559. doi: 10.1080/07350015.2018.1506926
    [33] Minnier J, Tian L, Cai T (2011) A perturbation method for inference on regularized regression estimates. J Ame Stat Assoc 106: 1371-1382. doi: 10.1198/jasa.2011.tm10382
    [34] Müller U (2014) HAC corrections for strongly autocorrelated time series. J Bus Econ Stat 32: 311-322. doi: 10.1080/07350015.2014.931238
    [35] Nelson CR, Kim MJ (1993) Predictable stock returns: the role of small sample bias. J Financ 48: 641-661. doi: 10.1111/j.1540-6261.1993.tb04731.x
    [36] Newey WK, West KD (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55: 703-708. doi: 10.2307/1913610
    [37] Polk C, Thompson S, Vuolteenaho T (2006) Cross-sectional forecast of the equity premium. J Financ Econ 81: 101-141. doi: 10.1016/j.jfineco.2005.03.013
    [38] Rozeff M (1984) Dividend yields are equity risk premium. J Portf Manage 11: 68-75. doi: 10.3905/jpm.1984.408980
    [39] Salibian-Barrera M, Zamar R (2002) Boostrapping robust estimates of regression. Dividend yields are equity risk premium. Ann Stat 30: 556-582.
    [40] Shao X (2010) The dependent wild bootstrap. J Am Stat Assoc 105: 218-235. doi: 10.1198/jasa.2009.tm08744
    [41] Shiller RJ (2000) . Princeton The dependent wild bootstrap, University Press, Princeton, NJ.
    [42] Singh K (1998) Breakdown theory for bootstrap quantiles. Ann Stat 26: 1719-1732.
    [43] Zhu K (2016) Breakdown Bootstrapping the portmanteau tests in weak autoregressive moving average models. J Royal Stat Soc 78: 463-485. doi: 10.1111/rssb.12112
    [44] Zhu K (2019) Statistical inference for autoregressive models under heteroskedasticity of unknown form. Ann Stat, In press.
    [45] Zhu K, Li WK (2015) A bootstrapped spectral test for adequacy in weak ARMA models. J Econom 187: 113-130. doi: 10.1016/j.jeconom.2015.02.005
    [46] Zhu K, Ling S (2015) LADE-based inference for ARMA models with unspecified and heavy-tailed heteroskedastic noises. J Am Stat Assoc 110: 784-794. doi: 10.1080/01621459.2014.977386
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2871) PDF downloads(735) Cited by(0)

Article outline

Figures and Tables

Figures(1)  /  Tables(5)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog