SimSMARTA: Simulation of the target stationary processes using the...

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

Description

Simulation of the target stationary processes using an SMARTA model to simulate the auxiliary Gaussian process and establish the target correlation structure. This model allows also the simulation of a multivariate process.

Usage

SimSMARTA(SMARTApar, steps, SMALAG = 512)

Arguments

SMARTApar	A list containing the parameters of the model. The list is constructed by the function "EstSMARTA".
steps	A scalar specifying the length of the time series to be generated.
SMALAG	A scalar specifying the order of the SMARTA model (must be equal to FFTAG and the lengths of ACFs).

Value

A list of the 3 simulated time series (in matrix format - i.e., matrix of dimensions steps x k, where steps denotes the length of generated time series and k the number of processes). X: The final time series at the actual domain with the target marginal distribution and correlation structure; Z: The auxiliary Gaussian time series at the Gaussian domain and; U: The auxiliary uniform time series at the Copula domain (i.e., in [0,1]).

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.