stcov: Space-time covariance function

In starma: Modelling Space Time AutoRegressive Moving Average (STARMA) Processes

Description

stcov computes the space-time covariance of the serie data between slag1-th and slag2-th order neighbours at time lag tlag.

Usage

stcov(data, wlist, slag1, slag2, tlag)

Arguments

data	a matrix or data frame containing the space-time series: row-wise should be the temporal observations, with each column corresponding to a site.
wlist	a list of the weight matrices for each k-th order neighbours, first one being the identity.
slag1, slag2	the space lags for the space-time covariance.
tlag	the time lag for the space-time covariance.

Details

stcov is mainly used as an internal function for the computation of stacf and stpacf. slag1 and slag2 must be lower than length(wlist).

It is computed as follows:

gamma[lk](s) = Tr ( ∑_[t=s+1]^[T] ( t(W[k]) * W[l] * z(t) * t(z(t-k)) )) / N(T-s)

Value

A numeric.

Author(s)

Felix Cheysson

References

Pfeifer, P., & Deutsch, S. (1980). A Three-Stage Iterative Procedure for Space-Time Modeling. Technometrics, 22(1), 35-47. doi:10.1080/00401706.1980.10486099

Examples

data(nb_mat)	# Get neighbourhood matrices

data <- matrix(rnorm(9400), 100, 94)

# Compute covariance between 2-nd and 1-st order neighbours, at time lag 5
stcov(data, blist, 2, 1, 5)		

Example output

[1] 0.005537725

starma documentation built on May 2, 2019, 1:26 p.m.