Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A space-time covariance function for spatio-temporal random processes
  and spatio-temporal prediction (kriging)   We consider a stationary spatio-temporal random process and assume that we
have a sample. By defining a sequence of discrete Fourier transforms at
canonical frequencies at each location, and using these complex valued random
varables as observed sample, we obtain expressions for the spatio-temporal
covariance functions and the spectral density functions of the spatio-temporal
random processes. These spectra correspond to non separable class of random
processes. The spatio-temporal covariance functions, obtained here are
functions of the spatial distance and the temporal frequency and are similar to
Matern class. These are in terms of modified Bessel functions of the second
kind. and the parameters are in terms of the second order spectral density
functions of the random proces and the spatial distances. We consider the
estimation of the parameters of the covariance function and also briefly
mention their asymptotic properties. The estimation of the entire data at a
known location, and also the estimation of a value given the above sample is
also considered. The predictors are obtained using the vectors of Discrete
Fourier Transforms. We also describe a statistical test for testing the
independence of the m spatial time series (testing for spatial independence)
using the Finite Fourier Transforms and it is based on the likelihood ratio
test of complex valued random variables The methods are illustrated with real
data.
  Keywords: Discrete Fourier Transforms, Covariance functions, Spectral density
functions, Space-Time Processses, Prediction(kriging) Laplacian operators,
Frequency Variogram, Tests for independence, Whittle likelihood.

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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph