portes (version 1.04)

simvarma: Simulate Data From ARMA(p,q) or VARMA(p,q) Models

Description

Simulate time series from AutoRegressive Moving Average, ARMA$(p,q)$, or Vector AutoRegressive Moving Average, VARMA$(p,q)$.

Usage

simvarma(phi=NULL,theta=NULL,sigma,intercept=NA,n,
         StableParameters=NA,Trunc.Series=NA)

Arguments

phi

a numeric or an array of AR or an array of VAR parameters with order $p$.

theta

a numeric or an array of MA or an array of VMA parameters with order $q$.

sigma

variance of white noise series. It must be entered as matrix in case of bivariate or multivariate time series.

intercept

the mean vector of the series.

n

length of the series.

StableParameters

the four parameters, ALPHA, BETA, GAMMA, and DELTA, as described in the function rstable. This argument is needed to generate model with innovations assumed to have stabl

Trunc.Series

truncation lag is used to truncate the infinite MA or VMA Process. IF it is NA, then Trunc.Series = min(100,$n/3$).

Value

• Simulated data from ARMA$(p,q)$ or VARMA$(p,q)$ process with errors that have stable Paretian or Gaussian distribution.

References

Hipel, K.W. and McLeod, A.I. (2005). "Time Series Modelling of Water Resources and Environmental Systems". Reinsel, G. C. (1997). "Elements of Multivariate Time Series Analysis". Springer-Verlag, 2nd edition.

See Also

arima.sim, simvma, ImpulseVMA, InvertQ, FitStable, rstable

Examples

########################################################################
# Simulate AR(2) process with phi = c(1.3, -0.35), Gaussian innovations
# The series is truncated at lag 40
Trunc.Series <- 40
n <- 200
sigma <- 1
intercept <- NA
phi <- c(1.3, -0.35)
theta <- NULL
simvarma(phi, theta, sigma, intercept, n, StableParameters=NA,Trunc.Series)
########################################################################
# Simulate a bivariate VARMA(1,1) process with length 300. 
# phi = array(c(0.5,0.4,0.1,0.5), dim=c(k,k,1)),
# theta = array(c(0,0.25,0,0), dim=c(k,k,1)).
# The innovations have normal distribution with mean c(10,12)
# The variance covariance is sigma = matrix(c(1,0.71,0.71,2),2,2).
# The series is truncated at default value: Trunc.Series=ceiling(100/3)=34 
k <- 2
n <- 300
Trunc.Series <-  50   
phi <-  array(c(0.5,0.4,0.1,0.5),dim=c(k,k,1))
theta <-  array(c(0,0.25,0,0),dim=c(k,k,1))
intercept <- c(10,12)
sigma <- matrix(c(1,0.71,0.71,2),k,k)
simvarma(phi,theta,sigma,intercept,n)
########################################################################
# Simulate univariate ARMA(2,1) process with length 500, 
# phi = c(1.3, -0.35), theta = 0.1.
# Stable innovations with: ALPHA = 1.75, BETA = 0, GAMMA = 1, DELTA = 0
n <- 500
phi <-  c(1.3, -0.35)
theta <-  0.1
intercept <- 0
sigma <-  0.7
ALPHA <- 1.75
BETA <- 0
GAMMA <- 1
DELTA <- 0
StableParameters <- c(ALPHA,BETA,GAMMA,DELTA)
simvarma(phi,theta,sigma,intercept,n,StableParameters)
########################################################################
# Simulate a bivariate VAR(1) process with length 100. 
# Stable Paretian: ALPHA=(1.3,1.6), BETA=(0,0.2), GAMMA=(1,1), DELTA=(0,0.2)
# The series is truncated at default value: Trunc.Series=min(100,200)=100 
k <- 2
n <- 600
phi <- array(c(-0.2,-0.6,0.3,1.1),dim=c(k,k,1))
theta <- NULL
sigma <- matrix(c(1,0.71,0.71,2),k,k)
intercept <- rep(0,k)
ALPHA <- c(1.3,1.6)
BETA <- c(0,0.2)
GAMMA <-c(1,1)
DELTA <-c(0,0.2)
StableParameters <- c(ALPHA,BETA,GAMMA,DELTA)
simvarma(phi,theta,sigma,intercept,n,StableParameters)