SimARTAp: Simulation of stationary process via ARTA(p) model.

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

Description

Simulation of stationary process with target marginal distribution and autocorrelation structure via ARTA(p) model.

Usage

SimARTAp(ARTApar, burn = 1000, steps = 10000, stand = F)

Arguments

ARTApar	A list containing the parameters of the model. The list is generated by function "EstARTAp".
burn	A scalar specifying the length of burn-out sample.
steps	A scalar specifying the length of the time series to be generated.
stand	A boolean (T or F) indicating whether to standardize (or not) the auxiliary Gaussian time series prior to their mapping to the actual domain. The default value is FALSE.

Value

A list of the 3 generated time series (in vector format): X: The final time series at the target 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

## Simulation of univariate stationary process with Gamma marginal distribution 
## and autocorrelation structure given by the product of a CAS and a periodic ACS.
## Not run: 
set.seed(12)

# Define the target autocorrelation structure.
acsS=csCAS(param=c(3,0.6),lag=1000) # Stationary CAS with b=3 and k=0.6.
acsP=csPeriodic(param=c(12,1.5),lag=1000) # Periodic ACS with p=12 and l=1.5.
ACS=csP*acsS # The target ACS as product of the two previous ones.

# Define the target distribution function (ICDF).
FX='qgamma' # the Gamma distribution

# Define the parameters of the target distribution.
pFX=list(shape=5,scale=1)

# Estimate the parameters of the auxiliary Gaussian AR(p) model.
ARTApar=EstARTAp(ACF=ACS,maxlag=0,dist=FX,params=pFX,NatafIntMethod='GH')

# Generate a synthetic series of 10000 length. 
SynthARTAcont=SimARTAp(ARTApar=ARTApar,steps=10^5)

## End(Not run)

## Simulation of univariate stationary process with discrete marginal distribution
## (Beta-Binomial) and autocorrelation structure given by CAS.
## Not run: 
set.seed(16)

# Define the target autocorrelation structure.
ACS=acsCAS(param=c(1.5,0.3),lag=1000) # CAS with b=1.5 and k=0.3.

# Define the target distribution function (ICDF).
require(TailRank)
FX='qbb' # the Beta-Binomial distribution.

# Define the parameters of the target distribution.
pFX=list(N=10,u=3,v=10)

# Estimate the parameters of the auxiliary Gaussian AR(p) model.
ARTApar=EstARTAp(ACF=ACS,maxlag=0,dist=FX,params=pFX,NatafIntMethod="MC")

# Generate a synthetic series of 10000 length. 
SynthARTAdiscr=SimARTAp(ARTApar=ARTApar,steps=10^5)

## End(Not run)

## Simulation of univariate stationary process with zero-inflated marginal distribution 
## (Gen. Gamma for the continuous part) and autocorrelation structure given by CAS.
## Not run: 
set.seed(18)

# Define the target autocorrelation structure.
ACS=acsCAS(param=c(0.91,1.09),lag=1000) # CAS with b=0.91 and k=1.09.

# Define the target distribution function (ICDF).
FX='qmixed' # Define that distribution is of zero-inflated type.

# Define the distribution for the continuous part of the process.
# Here, a re-parameterized version of Gen. Gamma distribution is used.
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 zero-inflated distribution function.
pFX=list(Distr=qgengamma,p0=0.8,scale=0.25,shape1=1.16,shape2=0.54) 

# Estimate the parameters of the auxiliary Gaussian AR(p) model.
ARTApar=EstARTAp(ACF=ACS,dist=FX,params=pFX,NatafIntMethod="GH",NoEval=9,polydeg=0)

# Generate a synthetic series of 10000 length. 
SynthARTAzi=SimARTAp(ARTApar=ARTApar,steps=10^5)

## End(Not run)

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