ARIMAdec {tsdecomp}

ARIMA-Model-Based Decomposition of Time Series

Description

This is the main function for the ARIMA-model-based decomposition of a time series.

Usage

ARIMAdec(x, mod, width = c(0.035, 0.035), min.modulus = 0.4, 
  extend = 16, drift = FALSE, optim.tol = 1e-04, ...)
## S3 method for class 'ARIMAdec'
print(x, units = c("radians", "degrees", "pi"), digits = 4, ...)
## S3 method for class 'ARIMAdec'
plot(x, ...)

Arguments

x

for ARIMAdec, a univariate time series; for plot.ARIMAdec and print.ARIMAdec, an object of class ARIMAdec returned by ARIMAdec.

mod

an object of class Arima. See arima.

width

numeric of length two, width of the interval of frequencies allocated to the trend and the seasonal components (measured in radians). If a numeric of length one is passed as argument, the same width is used for both components. See roots.allocation.

min.modulus

numeric, minimum modulus of the roots assigned to the trend component. See roots.allocation.

extend

integer; if greater than zero, the series is extended by means of forecasts and backcasts based on the fitted model mod. See filtering.

drift

logical, if TRUE the intercept in the fitted model mod or an external regressor named "drift" is treated as a deterministic linear trend. See filtering.

optim.tol

numeric, the convergence tolerance to be used by optimize.

units

character, the units in which the argument of the roots are printed. units="pi" prints the argument in radians as multiples of \pi.

digits

numeric, the number of significant digits to be used by print.

...

further arguments to be passed to poly2acgf or to plot.tsdecFilter and print methods.

Details

This function is a wrapper to the sequence of calls to roots.allocation, pseudo.spectrum, canonical.decomposition and filtering.

Value

An object of class ARIMAdec containing the following: 1) ar: the output from {roots.allocation}, 2) spectrum: the output from {pseudo.spectrum}, 3) ma: the output from {canonical.decomposition}, 4) xextended: the series extended with backcasts and forecasts (if extend > 0), 5) filters: the filters returned by {filtering}, 6) components: the estimated components returned by {filtering}.

References

Burman, J. P. (1980) ‘Seasonal Adjustment by Signal Extraction’. Journal of the Royal Statistical Society. Series A (General), 143(3), pp. 321-337. doi: 10.2307/2982132

Hillmer, S. C. and Tiao, G. C. (1982) ‘An ARIMA-Model-Based Approach to Seasonal Adjustment’. Journal of the American Statistical Association, 77(377), pp. 63-70. doi: 10.1080/01621459.1982.10477767

See Also

canonical.decomposition, filtering, pseudo.spectrum, roots.allocation.

Examples

# Airlines model and monthly data
y <- log(AirPassengers)
fit <- arima(y, order=c(0,1,1), seasonal=list(order=c(0,1,1)))
dec <- ARIMAdec(y, fit, extend=72)
dec
plot(dec)

# JohnsonJohnson quarterly data
y <- log(JohnsonJohnson)
fit <- arima(y, order=c(0,1,1), seasonal=list(order=c(0,1,1)))
dec <- ARIMAdec(y, fit, extend=16)
dec
plot(dec)

# Nile annual data
# this series is better modelled as a level shift at 
# observation 29 and a mean (no ARMA structure),
# here the shift is ignored for illustration of the 
# decomposition of the fitted ARIMA(0,1,1) model
y <- Nile
fit <- arima(y, order=c(0,1,1))
dec <- ARIMAdec(y, fit, extend=72)
dec
plot(dec, overlap.trend=TRUE, args.trend=list(col="blue"))