| stcov {starma} | R Documentation |
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. |
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)
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)