D. Mondal and D. B. Percival (2010), `Wavelet Variance Analysis for Gappy Time Series,' Annals of the Institute of Statistical Mathematics, 62, no. 5, pp. 943-966.

Summary

The wavelet variance is a scale-based decomposition of the process variance for a time series and has been used to analyze, for example, time deviations in atomic clocks, variations in soil properties in agricultural plots, accumulation of snow fields in the polar regions and marine atmospheric boundary layer turbulence. We propose two new unbiased estimators of the wavelet variance when the observed time series is `gappy,' i.e., is sampled at regular intervals, but certain observations are missing. We deduce the large sample properties of these estimators and discuss methods for determining an approximate confidence interval for the wavelet variance. We apply our proposed methodology to series of gappy observations related to atmospheric pressure data and Nile River minima.

Key Words

Asympototic normality; Confidence interval; Daubechies wavelet filter; Fractionally differenced process; Intrinsic stationarity; Kolmogorov turbulence; Nile River minima; Semi-variogram; Stationary process; TAO data; Wavelet cross-covariance

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