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Resampling time series by missing values techniques

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  • Alonso Fernández, Andrés Modesto
  • Peña, Daniel
  • Romo, Juan

Abstract

For strongly dependent data, deleting blocks of observations is expected to produce bias as in the moving block jackknife of KOnsch (1989) and Liu and Singh (1992). We propose an alternative technique which considers the blocks of deleted observations in the blockwise jackknife as missing data which are replaced by missing values estimates incorporating the observations dependence structure. Thus, the variance estimator is a weighted sample variance of the statistic evaluated in a "complete" series. We establish consistency for the variance and distribution of the sample mean. Also we extent this missing values approach to the blockwise bootstrap by assuming some missing observations among two consecutive blocks. We present the results of an extensive Monte Carlo study to evaluate the performance of the proposed methods in finite sample sizes in which it is shown that our proposal produces estimates of the variance of several time series statistics with smaller mean squared error than previous procedures.

Suggested Citation

  • Alonso Fernández, Andrés Modesto & Peña, Daniel & Romo, Juan, 2000. "Resampling time series by missing values techniques," DES - Working Papers. Statistics and Econometrics. WS 9923, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:9923
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    References listed on IDEAS

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    1. Pena, Daniel, 1990. "Influential Observations in Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 235-241, April.
    2. E. J. Hannan & L. Kavalieris, 1986. "Regression, Autoregression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 27-49, January.
    3. Bovas Abraham & A. Thavaneswaran, 1991. "A nonlinear time series model and estimation of missing observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(3), pages 493-504, September.
    4. Arup Bose, 1990. "Bootstrap in moving average models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(4), pages 753-768, December.
    5. Shao, Qi-Man & Yu, Hao, 1993. "Bootstrapping the sample means for stationary mixing sequences," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 175-190, October.
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    1. Alonso Fernández, Andrés Modesto & Peña, Daniel & Romo, Juan, 2001. "Introducing model uncertainty in time series bootstrap," DES - Working Papers. Statistics and Econometrics. WS ws011409, Universidad Carlos III de Madrid. Departamento de Estadística.

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    Keywords

    Jackknife;

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