Description Usage Arguments Value Author(s) Examples
It computes the spatio-temporal covariance matrix for balanced data, i.e., when we have the same temporal indexes per location. To compute the spatial correlation it provides 5 functions: exponential, gaussian, matern, spherical and power exponential. To compute the temporal correlation is used an autocorrelation function of an AR(1) process.
1 | CovarianceM(phi, rho, tau2, sigma2, distSpa, disTemp, kappa, type.S)
|
phi |
value of the spatial scaling parameter. |
rho |
value of the time scaling parameter. |
tau2 |
value of the the nugget effect parameter. |
sigma2 |
value of the partial sill. |
distSpa |
n x n spatial distance matrix without considering repetitions. |
disTemp |
T x T temporal distance matrix without considering repetitions. |
kappa |
parameter for all spatial covariance functions. In the case of exponential, gaussian and spherical function κ is equal to zero. For the power exponential function κ is a number between 0 and 2. For the matern correlation function is upper than 0. |
type.S |
type of spatial correlation function: ' |
The function returns the nT x nT spatio-temporal covariance matrix for balanced data.
Katherine L. Valeriano, Victor H. Lachos and Larissa A. Matos
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | # Initial parameter values
phi <- 5; rho <- 0.45
tau2 <- 0.80; sigma2 <- 2
# Simulating data
n1 <- 10 # Number of spatial locations
n2 <- 5 # Number of temporal index
set.seed(1000)
x.co <- round(runif(n1,0,10),5) # X coordinate
y.co <- round(runif(n1,0,10),5) # Y coordinate
coord <- cbind(x.co,y.co) # Cartesian coordinates without repetitions
time <- as.matrix(seq(1,n2)) # Time index without repetitions
# Covariance matrix
Ms <- as.matrix(dist(coord)) # Spatial distances
Mt <- as.matrix(dist(time)) # Temporal distances
Cov <- CovarianceM(phi,rho,tau2,sigma2,distSpa=Ms,disTemp=Mt,kappa=0,type.S="exponential")
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