fracdiff: fracdiff.sim – R documentation

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fracdiff.sim

Simulate fractional ARIMA Time Series

Description

Generates simulated long-memory time series data from the fractional ARIMA(p,d,q) model. This is a test problem generator for fracdiff.

Note that the MA coefficients have inverted signs compared to other parametrizations, see the details in fracdiff.

Usage

fracdiff.sim(n, ar = NULL, ma = NULL, d,
             rand.gen = rnorm, innov = rand.gen(n+q, ...),
             n.start = NA, backComp = TRUE, allow.0.nstart = FALSE,
             start.innov = rand.gen(n.start, ...),
             ..., mu = 0)

Arguments

`n`	length of the time series.
`ar`	vector of autoregressive parameters; empty by default.
`ma`	vector of moving average parameters; empty by default.
`d`	fractional differencing parameter.
`rand.gen`	a function to generate the innovations; the default, `rnorm` generates white N(0,1) noise.
`innov`	an optional times series of innovations. If not provided, `rand.gen()` is used.
`n.start`	length of “burn-in” period. If `NA`, the default, the same value as in `arima.sim` is computed.
`backComp`	logical indicating if back compatibility with older versions of `fracdiff.sim` is desired. Otherwise, for `d = 0`, compatibility with R's `arima.sim` is achieved.
`allow.0.nstart`	logical indicating if `n.start = 0` should be allowed even when p + q > 0. This not recommended unless for producing the same series as with older versions of `fracdiff.sim`.
`start.innov`	an optional vector of innovations to be used for the burn-in period. If supplied there must be at least `n.start` values.
`...`	additional arguments for `rand.gen()`. Most usefully, the standard deviation of the innovations generated by `rnorm` can be specified by `sd`.
`mu`	time series mean (added at the end).

Value

a list containing the following elements :

`series`	time series
`ar, ma, d, mu, n.start`	same as input

Examples

## Pretty (too) short to "see" the long memory
fracdiff.sim(100, ar = .2, ma = .4, d = .3)

## longer with "extreme" ar:
r <- fracdiff.sim(n=1500, ar=-0.9, d= 0.3)
plot(as.ts(r$series))

## Show that  MA  coefficients meaning is inverted
## compared to   stats :: arima :

AR <- 0.7
MA <- -0.5
n.st <- 2

AR <- c(0.7, -0.1)
MA <- c(-0.5, 0.4)
n <- 512 ; sd <- 0.1
n.st <- 10

set.seed(101)
Y1 <- arima.sim(list(ar = AR, ma = MA), n = n, n.start = n.st, sd = sd)
plot(Y1)

# For our fracdiff, reverse the MA sign:
set.seed(101)
Y2 <- fracdiff.sim(n = n, ar = AR, ma = - MA, d = 0,
                   n.start = n.st, sd = sd)$series
lines(Y2, col=adjustcolor("red", 0.5))
## .. no, you don't need glasses ;-)  Y2 is Y1 shifted slightly

##' rotate left by k (k < 0: rotate right)
rot <- function(x, k) {
  stopifnot(k == round(k))
  n <- length(x)
  if(k <- k %% n) x[c((k+1):n, 1:k)] else x
}
k <- n.st - 2
Y2.s <- rot(Y2, k)
head.matrix(cbind(Y1, Y2.s))
plot(Y1, Y2.s); i <- (n-k+1):n
text(Y1[i], Y2.s[i], i, adj = c(0,0)-.1, col=2)

## With  backComp = FALSE,  get *the same* as arima.sim():
set.seed(101)
Y2. <- fracdiff.sim(n = n, ar = AR, ma = - MA, d = 0,
                    n.start = n.st, sd = sd, backComp = FALSE)$series
stopifnot( all.equal( c(Y1), Y2., tolerance= 1e-15))

fracdiff

Fractionally Differenced ARIMA aka ARFIMA(P,d,q) Models

v1.5-1

GPL (>= 2)

Authors

Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Chris Fraley [ctb, cph] (S original; Fortran code), Friedrich Leisch [ctb] (R port, <https://orcid.org/0000-0001-7278-1983>), Valderio Reisen [ctb] (fdGPH() & fdSperio()), Artur Lemonte [ctb] (fdGPH() & fdSperio()), Rob Hyndman [ctb] (residuals() & fitted(), <https://orcid.org/0000-0002-2140-5352>)

Initial release

2020-01-20