Wavelet Analysis Of Spatio-Temporal Data
This paper aims to provide a wavelet analysis for spatio-temporal data which are observed on irregularly spaced stations at discrete time points, where the spatial covariances show serious non-stationarity caused by local dependency. A specific example that is used for the demonstration is US precipitation data observed on about ten thousand stations in every month. By a reinterpretation of Whittle likelihood function for stationary time series, we propose a kind of Bayesian regression model for spatial data whose regressors are given by modified Haar wavelets and try a spatio-temporal extension by a state space approach. We also propose an empirical Bayes estimation for the parameters, which is regarded as a spatio-temporal extension of Whittle likelihood estimation originally defined for stationary time series. We conduct the extended Whittle estimate and compare mean square errors of the forecasts with those of some benchmarks to evaluate its goodness for the US precipitation data in August from 1987-1997.
|Date of creation:||Jan 2014|
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- Kaufman, Cari G. & Schervish, Mark J. & Nychka, Douglas W., 2008. "Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1545-1555.
- Sudipto Banerjee & Alan E. Gelfand & Andrew O. Finley & Huiyan Sang, 2008. "Gaussian predictive process models for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 825-848.
- Yun Bai & Peter X.-K. Song & T. E. Raghunathan, 2012. "Joint composite estimating functions in spatiotemporal models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(5), pages 799-824, November.
- Gneiting T., 2002. "Nonseparable, Stationary Covariance Functions for Space-Time Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 590-600, June.
- G. P. Nason & R. von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
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