armaimp {timsac}R Documentation

Caluculate Characteristics of Scalar ARMA Model

Description

Caluculate impulse, autocovariance, partial autocorrelation function and characteristic roots of scalar ARMA model for given AR and MA coefficients.

Usage

  armaimp( arcoef, macoef, v, n=1000, lag=NULL, nf=200, plot=TRUE )

Arguments

arcoef AR coefficients.
macoef MA coefficients.
v innivation variance.
n data length.
lag maximum lag of autocovariance function. Default is 2*sqrt(n).
nf number of frequencies in evaluating spectrum.
plot logical. If TRUE (default) impulse response function, autocovariance, power spectrum and characteristic roos are plotted.

Details

The ARMA model is given by

y(t) - a(1)y(t-1) - ... - a(p)y(t-p) = u(t) - b(1)u(t-1) - ... - b(q)u(t-q),

where p is AR order, q is MA order and u(t) is a zero mean white noise.

Value

impuls impulse response function.
acov autocovariance function.
parcor partial autocorrelation function.
spec power spectrum.
croot.ar characteristic roots of AR operator. Chracteristic root is a list with components named real(real part R), image(imaginary part I), amp(=sqrt(R**2+I**2)), atan(=ARCTAN(I/R)) and degree.
croot.ma characteristic roots of MA operator.

References

G.Kitagawa (1993) Time series analysis programing (in Japanese). The Iwanami Computer Science Senes.

Examples

  # ARMA model : y(n) = 0.9sqrt(3)y(n-1) - 0.81y(n-2) + v(n) -0.9sqrt(2)v(n-1) + 0.81v(n-2)
  a <- c(0.9*sqrt(3), -0.81)
  b <- c(0.9*sqrt(2), -0.81)
  z <- armaimp( arcoef=a, macoef=b, v=1.0, n=1000, lag=20 )
  z$croot.ar
  z$croot.ma

  # AR model : y(n) = 0.9sqrt(3)y(n-1) - 0.81y(n-2) + v(n)
  z <- armaimp( arcoef=a, v=1.0, n=1000, lag=20 )
  z$croot.ar

  # MA model : y(n) = v(n) -0.9sqrt(2)v(n-1) + 0.81v(n-2)
  z <- armaimp( macoef=b, v=1.0, n=1000, lag=20 )
  z$croot.ma

[Package timsac version 1.2.1 Index]