sarima.sim {astsa}

ARIMA Simulation

Description

Simulate data from (seasonal) ARIMA models.

Usage

sarima.sim(ar = NULL, d = 0, ma = NULL, sar = NULL, D = 0, sma = NULL, S = NULL, 
            n = 500, rand.gen = rnorm, innov = NULL, burnin = NA, t0 = 0, ...)

Arguments

ar

coefficients of AR component (does not have to be specified)

d

order of regular difference (does not have to be specified)

ma

coefficients of MA component (does not have to be specified)

sar

coefficients of SAR component (does not have to be specified)

D

order of seasonal difference (does not have to be specified)

sma

coefficients of SMA component (does not have to be specified)

S

seasonal period (does not have to be specified)

n

desired sample size (defaults to 500)

rand.gen

optional; a function to generate the innovations (defaults to normal)

innov

an optional times series of innovations. If not provided, rand.gen is used.

burnin

length of burn-in (a non-negative integer). If NA (the default) a reasonable value is selected.

t0

start time (defaults to 0)

...

additional arguments applied to the innovations. For rand.gen, the standard deviation of the innovations generated by rnorm can be specified by sd or the mean by mean (see details and examples). In addition, rand.gen may be overridden using a preset sequence of innovations specifying innov (see details and examples).

Details

Will generate a time series of length n from the specified SARIMA model using simplified input.

The use of the term mean in ... refers to the generation of normal innovations. For example, sarima.sim(ar=.9, mean=5) will generate data using N(5,1) or 5+N(0,1) innovations, so that the constant in the model is 5 and the mean of the AR model is 5/(1-.9) = 50. In sarima.sim(ma=.9, mean=5), however, the model mean is 5 (the constant). Also, a random walk with drift = .1 can be generated by sarima.sim(d=1, mean=.1, burnin=0), which is equivalent to cumsum(rnorm(500, mean=.1)). The same story goes if sd is specified; i.e., it's applied to the innovations. Because anything specified in ... refers to the innovations, a simpler way to generate a non-zero mean is to add the value outside the call; see the examples.

If innov is used to input the innovations and override rand.gen, be sure that length(innov) is at least n + burnin. If the criterion is not met, the script will return less than the desired number of values and a warning will be given.

Value

A time series of length n from the specified SARIMA model with the specified frequency if the model is seasonal and start time t0.

Note

The model autoregressive polynomial ('AR side' = AR x SAR) is checked for causality and the model moving average polynomial ('MA side' = MA x SMA) is checked invertibility. The script stops and reports an error at the first violation of causality or invertibility; i.e., it will not report multiple errors.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## AR(2) with mean 50 [n = 500 is default]
y = sarima.sim(ar=c(1.5,-.75)) + 50
tsplot(y)

## ARIMA(0,1,1) with drift ['mean' refers to the innovations] 
tsplot(sarima.sim(ma=-.8, d=1, mean=.1))

## SAR(1) example from text
set.seed(666)   # not that 666
sAR = sarima.sim(sar=.9, S=12, n=36)
tsplot(sAR, type='c')
points(sAR, pch=Months, cex=1.1, font=4, col=1:4)

## SARIMA(0,1,1)x(0,1,1)_12 - B&J's favorite
set.seed(101010)
tsplot(sarima.sim(d=1, ma=-.4, D=1, sma=-.6, S=12, n=120))  

## infinite variance t-errors 
tsplot(sarima.sim(ar=.9, rand.gen=function(n, ...) rt(n, df=2) ))

## use your own innovations
dog = rexp(150, rate=.5)*sign(runif(150,-1,1))
tsplot(sarima.sim(n=100, ar=.99, innov=dog, burnin=50))

## generate seasonal data but no P, D or Q - you will receive 
## a message to make sure that you wanted to do this on purpose: 
tsplot(sarima.sim(ar=c(1.5,-.75), n=144, S=12), ylab='doggy', xaxt='n')
mtext(seq(0,144,12), side=1, line=.5, at=0:12)