starma (version 1.3)

stcov: Space-time covariance function

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.

Value

A numeric.

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: $$\hat{\gamma}_{lk}(s) = \frac{1}{N(T-s)} Tr \left( \sum_{t=s+1}^{T} W^{(k)\prime} W^{(l)} z_t z_{t-k}^\prime \right)$$

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)