ARIMAdec function

ARIMA-Model-Based Decomposition of Time Series

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

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.

Returns

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. tools:::Rd_expr_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. tools:::Rd_expr_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"))