EstSMARTA: Estimation of the auxiliary SMA model parameters

In itsoukal/anySim: Stochastic Simulation of Processes with any Marginal Distribution and Correlation Structure

Description

Estimation of parameters of the auxiliary SMA model to simulate the auxiliary Gaussian process.

Usage

EstSMARTA(
  dist,
  params,
  ACFs,
  Cmat,
  DecoMethod = "cor.smooth",
  FFTLag = 512,
  NatafIntMethod = "GH",
  NoEval = 9,
  polydeg = 8,
  ...
)

Arguments

dist	A k-dimensional string vector indicating the quantile function of the target marginal distribution (i.e., the ICDF).
params	A k-dimensional named list with the parameters of the target distributions.
ACFs	A k-dimensional list with the target autocorrelation structure (including lag-0, i.e., 1).
Cmat	A matrix (k x k) containing the lag-0 cross-correlation coefficients of the processes.
DecoMethod	A string indicating the decomposition method, in case of a non-positive definite matrix (options: 'cor.smooth' and 'nearPD')
FFTLag	A scalar indicating the length of the Fast Fourrier Transform (required to estimate the internal parameters of SMA model). Default value=512.
NatafIntMethod	A string ("GH", "Int", or "MC"), indicating the intergation method, to resolve the Nataf integral.
NoEval	A scalar (power of 2) indicating (default: 9) the number of evaluation points for the integration methods.
polydeg	A scalar indicating the order of the fitted polynomial. If polydeg=0, then another curve is fitted.
...	Additional named arguments for the selected "NatafIntMethod" method.

Value

A list with the parameters of the auxiliary Gaussian SMA model.

Note

Avoid the use of the "GH" method (i.e., NatafIntMethod='GH'), when the marginal(s) are discrete.

Examples

## Multivariate simulation of 3 stationary processes with specific distribution functions 
## and autocorrelation structures, as well as specific lag-0 cross-correlation matrix.
## Not run: 
set.seed(9)

# Define the target autocorrelation structure of the 3 processes.
ACSs=list()
ACSs[[1]]=csCAS(param=c(0.1,0.7),lag=2^6)
ACSs[[2]]=csCAS(param=c(0.2,1),lag=2^6)
ACSs[[3]]=csCAS(param=c(0.1,0.5),lag=2^6)

# Define the matrix of lag-0 cross-correlation coefficients between the 3 processes.
Cmat=matrix(c(1,0.4,-0.5,
              0.4,1,-0.3,
             -0.5,-0.3,1),ncol=3,nrow=3)

# Define the target distribution functions (ICDF) of the 3 processes
FXs=rep('qmixed',3) # Define that distributions are of zero-inflated type.

# Define the distributions for the continuous part of the processes. 
# In this example, a re-parameterized version of Gen. Gamma distribution is used for the second process.
qgengamma=function(p,scale, shape1, shape2){
  require(VGAM)
  X=qgengamma.stacy(p=p,scale=scale,k=(shape1/shape2),d=shape2)
  return(X)
}

# Define the parameters of the target distributions.
pFXs[[1]]=list(Distr=qbeta,p0=0,shape1=15,shape2=5) # Beta distribution
pFXs[[2]]=list(Distr=qgengamma,p0=0.7,scale=0.12, shape1=1.35, shape2=0.4) # Gen. Gamma
pFXs[[3]]=list(Distr=qnorm,p0=0,mean=15,sd=3) # Normal distribution

# Estimate the parameters of SMARTA model
SMAparam=EstSMARTA(dist=FXs,params=pFXs,ACFs=ACSs,Cmat=Cmat,
                   DecoMethod='cor.smooth',FFTLag = 2^7,
                   NatafIntMethod='GH',NoEval=9,polydeg=8)
                   
# Generate the synthetic series     
simSMARTA=SimSMARTA(SMARTApar=SMAparam,steps=2^14,SMALAG=2^6)

## End(Not run)

itsoukal/anySim documentation built on May 7, 2020, 11:57 p.m.