Resampling time series using missing values techniques |
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Authors: | Andrés M Alonso Daniel Peña Juan Romo |
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Institution: | (1) Department of Mathematics, Universidad Autónoma de Madrid, 28049 Madrid, Spain;(2) Department of Statistics and Econometrics, Universidad Carlos III de Madrid, 28903 Getafe, Spain |
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Abstract: | Several techniques for resampling dependent data have already been proposed. In this paper we use missing values techniques
to modify the moving blocks jackknife and bootstrap. More specifically, we consider the blocks of deleted observations in
the blockwise jackknife as missing data which are recovered by missing values estimates incorporating the observation dependence
structure. Thus, we estimate the variance of a statistic as a weighted sample variance of the statistic evaluated in a “complete”
series. Consistency of the variance and the distribution estimators of the sample mean are established. Also, we apply the
missing values approach to the blockwise bootstrap by including some missing observations among two consecutive blocks and
we demonstrate the consistency of the variance and the distribution estimators of the sample mean. Finally, we present the
results of an extensive Monte Carlo study to evaluate the performance of these methods for finite sample sizes, showing that
our proposal provides variance estimates for several time series statistics with smaller mean squared error than previous
procedures. |
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Keywords: | Jackknife bootstrap missing values time series |
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