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Draw a time series from a fitted spectrum

Source: R/spectral.R
frm_series_draw.Rd

The inverse of the transform a spectral fit is built on, and the verb to reach for when simulate() gave ordinates where a series was wanted. It draws a stationary Gaussian series whose spectral density is the one the fit estimated, by giving each Fourier frequency an independent complex Gaussian amplitude with the fitted variance and transforming back.

Usage

frm_series_draw(
  object,
  nsim = 1,
  seed = NULL,
  newdata = NULL,
  freq = "freq",
  ...
)

Arguments

object

A frmtmb_fit with a whittle() family.

nsim

Number of series to draw.

seed

Optional integer seed.

newdata

Rows to take the spectrum from, for a fit that pools several series. Defaults to the fitted rows.

freq

The frequencies, either as a column name in the data or as the numbers themselves. A model written in terms of a transformed frequency keeps no freq column, so passing pg$freq is the general route.

...

Passed to predict(), for example re_formula.

Value

A ts matrix with 2 * nf + 1 rows and nsim columns, at the sampling rate the grid implies.

Details

A simulated PERIODOGRAM cannot be inverted: the phases are not in it. What is well defined is a draw from the fitted MODEL, which is what this is, and it is a different object - two calls with the same fitted spectrum give two unrelated series.

The length is fixed by the grid at 2 * nf + 1, an odd number, so that the drawn series has no Nyquist ordinate to invent and exactly zero mean. The sampling rate follows from the grid spacing, and the result carries it as a ts frequency, so frm_periodogram(frm_series_draw(fit)) lands back on the same grid.

See also

whittle(), frm_periodogram().

Examples

set.seed(1)
y <- as.numeric(arima.sim(list(ar = 0.6), 512))
pg <- frm_periodogram(y, fs = 128)
fit <- frm(bf(pgram ~ s(freq, k = 8)), family = whittle(), data = pg)

# a new series with the same estimated spectrum, not the same series
z <- frm_series_draw(fit, nsim = 2, seed = 1)
dim(z)
#> [1] 511   2
stats::frequency(z)
#> [1] 127.75