Wavelet variance analysis for gappy time series |
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| Authors: | Debashis Mondal Donald B. Percival |
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| Affiliation: | (1) State Key Laboratory of Lake Science and Environment, Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, Nanjing, 210008, China;(2) National Climate Centre-Centre on Climate Change, China Meteorological Administration, Beijing, 100081, China;(3) School of Hydropower & Information Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China;(4) College of Territorial Resources and Tourism, Anhui Normal University, Wuhu, 241000, China;(5) Hydrological Bureau of the Jiangsu Province, Nanjing, 210029, China;(6) Graduate School of the Chinese Academy of Sciences, Beijing, 100039, China; |
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| Abstract: | 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. |
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