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VARIANCE ESTIMATION FOR SAMPLE AUTOCOVARIANCES: DIRECT AND RESAMPLING APPROACHES
Author(s) -
Hurvich Clifford M.,
Simonoff Jeffrey S.,
Zeger Scott L.
Publication year - 1991
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1991.tb00410.x
Subject(s) - jackknife resampling , resampling , mathematics , frequency domain , monte carlo method , covariance , statistics , series (stratigraphy) , gaussian , variance (accounting) , algorithm , estimator , mathematical analysis , paleontology , physics , accounting , quantum mechanics , business , biology
Summary The usual covariance estimates for data n‐1 from a stationary zero‐mean stochastic process { X t } are the sample covariances Both direct and resampling approaches are used to estimate the variance of the sample covariances. This paper compares the performance of these variance estimates. Using a direct approach, we show that a consistent windowed periodogram estimate for the spectrum is more effective than using the periodogram itself. A frequency domain bootstrap for time series is proposed and analyzed, and we introduce a frequency domain version of the jackknife that is shown to be asymptotically unbiased and consistent for Gaussian processes. Monte Carlo techniques show that the time domain jackknife and subseries method cannot be recommended. For a Gaussian underlying series a direct approach using a smoothed periodogram is best; for a non‐Gaussian series the frequency domain bootstrap appears preferable. For small samples, the bootstraps are dangerous: both the direct approach and frequency domain jackknife are better.