fitVAR: VAR model parameters to simulate correlated parent Gaussian...

In CoSMoS: Complete Stochastic Modelling Solution

VAR model parameters to simulate correlated parent Gaussian random vectors and fields

Description

Compute VAR model parameters to simulate parent Gaussian random vectors with specified spatiotemporal correlation structure using the method described by Biller and Nelson (2003).

Usage

fitVAR(
  spacepoints,
  p,
  margdist,
  margarg,
  p0,
  distbounds = c(-Inf, Inf),
  stcsid,
  stcsarg,
  scalefactor = 1,
  anisotropyid = "affine",
  anisotropyarg = list(phi1 = 1, phi2 = 1, phi12 = 0, theta = 0),
  advectionid = "uniform",
  advectionarg = list(u = 0, v = 0),
  dsid = "gauss",
  dsarg = NULL
)

Arguments

spacepoints	it can be a numeric integer, which is interpreted as the side length m of the square field (m x m), or a matrix (d x 2) of coordinates (e.g. longitude and latitude) of d spatial locations (e.g. d gauge stations)
p	order of VAR(p) model
margdist	target marginal distribution of the field
margarg	list of marginal distribution arguments. Please consult the documentation of the selected marginal distribution indicated in the argument margdist for the list of required parameters
p0	probability zero
distbounds	distribution bounds (default set to c(-Inf, Inf))
stcsid	spatiotemporal correlation structure ID
stcsarg	list of spatiotemporal correlation structure arguments. Please consult the documentation of the selected spatiotemporal correlation structure indicated in the argument stcsid for the list of required parameters
scalefactor	factor specifying the distance between the centers of two pixels (default set to 1)
anisotropyid	spatial anisotropy ID (affine by default, swirl or wave)
anisotropyarg	list of arguments characterizing the spatial anisotropy according to the syntax of the function anisotropyT. Isotropic fields by default
advectionid	advection field ID (uniform by default, rotation, spiral, spiralCE, radial, or hyperbolic)
advectionarg	list of arguments characterizing the advection field according to the syntax of advectionF. No advection by default
dsid	dependence structure ID (gauss by default, student, bardossy, and bardossyF)
dsarg	argument characterizing the dependence structure: NULL for gauss by default, number of degrees of freedom for student or parameter m in (-Inf, Inf) for bardossy (see Note section for more details)

Details

The fitting algorithm has O(m*m)^3 complexity for a (m*m) field or equivalently O(d^3) complexity for a d-dimensional vector. Very large values of (m*m) (or d) and high order AR correlation structures can be unpractical on standard machines.

Here, we give indicative CPU times for some settings, referring to a Windows 10 Pro x64 laptop with Intel(R) Core(TM) i7-6700HQ CPU @ 2.60GHz, 4-core, 8 logical processors, and 32GB RAM.
: CPU time:
d = 100 or m = 10, p = 1: ~ 0.4s
d = 900 or m = 30, p = 1: ~ 6.0s
d = 900 or m = 30, p = 5: ~ 47.0s
d = 2500 or m = 50, p = 1: ~100.0s

Note

While all the advection types can be applied to isotropic random fields, anisotropic random fields require more care. We suggest combining affine anysotropy with uniform advection, and swirl anisotropy with rotation or spiral advection with the same rotation center..
Concerning the Bardossy model, the increase of the parameter m leads to a more and more symmetrical copula, and if m tends to Inf, then the copula converges to the Gaussian copula. The bardossy model is characterized by lower tail dependence weaker than the upper tail dependence, while the flipped Bárdossy dependence structure, denoted as bardossyF, has lower tail dependence stronger than the upper tail dependence. See Bárdossy (2006) for more details about the properties and parametrization of the multivariate Bardossy distribution

References

Bárdossy, A. (2006), Copula-based geostatistical models for groundwater quality parameters, Water Resour. Res., 42, W11416, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1029/2005WR004754")}

Biller, B., Nelson, B.L. (2003). Modeling and generating multivariate time-series input processes using a vector autoregressive technique. ACM Trans. Model. Comput. Simul. 13(3), 211-237, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1145/937332.937333")}

Papalexiou, S.M. (2018). Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency. Advances in Water Resources, 115, 234-252, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.advwatres.2018.02.013")}

Papalexiou, S.M., Serinaldi, F. (2020). Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity. Water Resources Research, 56(2), e2019WR026331, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1029/2019WR026331")}

Papalexiou, S.M., Serinaldi, F., Porcu, E. (2021). Advancing Space-Time Simulation of Random Fields: From Storms to Cyclones and Beyond. Water Resources Research, 57, e2020WR029466, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1029/2020WR029466")}

Examples

## for multivariate simulation
coord <- cbind(runif(4)*30, runif(4)*30)

fit <- fitVAR(
  spacepoints = coord,
  p = 1,
  margdist ='burrXII',
  margarg = list(scale = 3,
                 shape1 = .9,
                 shape2 = .2),
  p0 = 0.8,
  stcsid = "clayton",
  stcsarg = list(scfid = "weibull",
                 tcfid = "weibull",
                 copulaarg = 2,
                 scfarg = list(scale = 20,
                               shape = 0.7),
                 tcfarg = list(scale = 1.1,
                               shape = 0.8))
)

dim(fit$alpha)
dim(fit$res.cov)

fit$m
fit$margarg
fit$margdist

## for random fields simulation
fit <- fitVAR(
  spacepoints = 10,
  p = 1,
  margdist ='burrXII',
  margarg = list(scale = 3, shape1 = .9, shape2 = .2),
  p0 = 0.8,
  stcsid = "clayton",
  stcsarg = list(scfid = "weibull", tcfid = "weibull",
                 copulaarg = 2,
                 scfarg = list(scale = 20, shape = 0.7),
                 tcfarg = list(scale = 1.1, shape = 0.8))
)

dim(fit$alpha)
dim(fit$res.cov)

fit$m
fit$margarg
fit$margdist

CoSMoS documentation built on May 8, 2026, 1:08 a.m.