Wavelet estimation for locally self-similar processes
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摘要: 首先, 针对时变自相似参数提出了一种基于最大重叠离散小波变换的估计方法; 对此进行了蒙特卡洛模拟研究, 发现提高了估计的精度; 最后, 将研究结果应用于海洋垂直切变序列.Abstract: A new estimation method was proposed based on the maximal overlap discrete wavelet transform, which provided a good alternative for the estimation of the time-varying self-similarity parameters. It also included a simulation-based study using Monte Carlo method, which increases the accuracy of the estimation. Finally, an application was made on the vertical ocean shear measurements.
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Key words:
- locally self-similar process /
- long memory /
- Monte Carlo simulation /
- OLS regression /
- wavelet transform
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[1] {1}WHITCHER B, JENSEN M J. Wavelet estimation of a local long memoryparameter[J]. Exploration Geophysics, 2000, 31: 94-103.{2}JENSEN M J. Using wavelets to obtain a consistent ordinary leastsquares estimator of the long memory parameter[J]. Journal ofForecasting, 1999, 18: 17-32.{3}CAVANAUGH J E, WANG Y, DAVIS J W. Locally self-similar processesand their wavelet analysis[M]. Handbook of statistics 21: StochasticProcesses: Modeling and Simulation. Amsterdam: Elsevier Science,2002.{4}COEURJOLLY J F. Hurst exponent estimation of locally self-similarGaussian processes using sample quantiles[J]. Annals of Statistics,2008, 36(3): 1404-1434.{5}LU Z, GUEGAN D. Estimation of time-varying long memory parameterusing wavelet method[J]. Communications in Statistics-Simulation andComputation, 2011, 40: 596-613.{6}PERCIVAL D B, WALDEN A T. Wavelet methods for time seriesanalysis[M]. Cambridge: Cambridge University Press, 2000.{7}PERCIVAL D B, GUTTORP P. Long Memory Processes, the Allan Varianceand Wavelets[M]. Wavelets in Geophysics. New York: Academic Press,1994.
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