  The covariance function and the variogram play very important roles in
modelling and in prediction of spatial and spatio-temporal data. The assumption
of second order stationarity, in space and time, is often made in the analysis
of spatial data and the spatio-temporal data. Several times the assumption of
stationarity is considered to be very restrictive, and therefore, a weaker
assumption that the data is Intrinsically stationary both in space and time is
often made and used, mainly by the geo-statisticians and other environmental
scientists. In this paper we consider the data to be intrinsically stationary.
Because of the inclusion of time dimension,the estimation and derivation of the
sampling properties of various estimators related to spatio-temporal data
become complicated. In this paper our object is to present an alternative way,
based on Frequency Domain methods for modelling the data. Here we consider
Discrete Fourier Transforms (DFT) defined for the (Intrinsic) time series data
observed at several locations as our data, and then consider the estimation of
the parameters of spatio-temporal covariance function, estimation of Frequency
Variogram, tests of independence etc. We use the well known property that the
Discrete Fourier Transforms of stationary time series evaluated at distinct
Fourier Frequencies are asymptotically independent and distributed as complex
normal in deriving many results considered in this paper.
