roots-allocation function

Allocation of Autoregressive Roots

Allocate the roots of the autoregressive polynomial from a fitted ARIMA model to trend, transitory and seasonal components.

roots.allocation(x, width = c(0.035, 0.035), min.modulus = 0.4)
## S3 method for class 'tsdecARroots'
plot(x, xlim, ylim, ...)
## S3 method for class 'tsdecARroots'
print(x, units = c("radians", "degrees", "pi"), digits = 4, ...)

Arguments

• x: for roots.allocation, an object of class Arima (see arima); for print.tsdecARroots and plot.tsdecARroots, an object of class tsdecARroots

  returned by type="roots.allocation".

• 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.

• min.modulus: numeric, minimum modulus of the roots assigned to the trend component.

• xlim: optional numerics, lower and upper limits of the x-axis.

• ylim: optional numerics, lower and upper limits of the y-axis.

• 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 plot or print.

Details

The roots related to cycles with frequency within the range [$0$, width[1]] are allocated to the trend or transitory component. In particular,if the modulus is below min.modulus, then they are are allocated to the transitory component, otherwise to the trend.

The seasonal frequencies are defined as $\omega[j]=2\pi j/S$, for $j=1,...,S-1$, where $S$ is the periodicity of the data (e.g., $S=4$ in quarterly data and $S=12$ in monthly data). Roots related to cycles of frequency within the range [$\omega[j] -$seasonal.width, $\omega[j] +$seasonal.width] are assigned to the seasonal component.

Returns

roots.allocation returns a list of class tsdecARroots. plot.tsdecARroots displays the roots in the complex plane and print.tsdecARroots shows a summary.