TY  - JOUR
T1  - Wavelet Methods in Interpolation of High-Frequency Spatial-Temporal Pressure
JF  - Spatial Statistics
Y1  - 2014
A1  - Chang,Xiaohui
A1  - Stein,Michael L.
KW  - Business Analytics
AB  - The location-scale and whitening properties of wavelets make them more favorable for interpolating high-frequency monitoring data than Fourier-based methods. In the past, wavelets have been used to simplify the dependence structure in multiple time or spatial series, but little has been done to apply wavelets as a modeling tool in a space–time setting, or, in particular, to take advantage of the localization of wavelets to capture the local dynamic characteristics of high-frequency meteorological data. This paper analyzes minute-by-minute atmospheric pressure data from the Atmospheric Radiation Measurement program using different wavelet coefficient structures at different scales and incorporating spatial structure into the model. This approach of modeling space–time processes using wavelets produces accurate point predictions with low uncertainty estimates, and also enables interpolation of available data from sparse monitoring stations to a high density grid and production of meteorological maps on large spatial and temporal scales.
VL  - 8
U2  - a
U4  - 99245645824
ID  - 99245645824
ER  - 

TY  - JOUR
T1  - Decorrelation Property of Discrete Wavelet Transform Under Fixed-Domain Asymptotics
JF  - IEEE Transactions on Information Theory
Y1  - 2013
A1  - Chang,Xiaohui
A1  - Stein,Michael L.
KW  - Business Analytics
AB  - Theoretical aspects of the decorrelation property of the discrete wavelet transform when applied to stochastic processes have been studied exclusively from the increasing-domain perspective, in which the distance between neighboring observations stays roughly constant as the number of observations increases. To understand the underlying data-generating process and to obtain good interpolations, fixed-domain asymptotics, in which the number of observations increases in a fixed region, is often more appropriate than increasing-domain asymptotics. In the fixed-domain setting, we prove that, for a general class of inhomogeneous covariance functions, with suitable choice of wavelet filters, the wavelet transform of a nonstationary process has mostly asymptotically uncorrelated components.
VL  - 59
U2  - a
U4  - 99245598720
ID  - 99245598720
ER  -