armaimp

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Calculate Characteristics of Scalar ARMA Model

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

Keywords
ts
Usage
armaimp(arcoef = NULL, macoef = NULL, v, n = 1000, lag = NULL, nf = 200,
        plot = TRUE, …)
Arguments
arcoef

AR coefficients.

macoef

MA coefficients.

v

innovation 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, parcor and characteristic roots are plotted.

further arguments to be passed to plot.arma.

Details

The ARMA model is given by

$$y_t - a_1y_{t-1} - \dots - a_py_{t-p} = u_t - b_1u_{t-1} - \dots - b_qu_{t-q},$$

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

Characteristic roots of AR / MA operator is a list with the following components:

  • re: real part \(R\)

  • im: imaginary part \(I\)

  • amp: \(\sqrt{R^2+I^2}\)

  • atan: \(\arctan(I/R)\)

  • degree

Value

An object of class "arma", which is a list with the following elements:

impuls

impulse response function.

acov

autocovariance function.

parcor

partial autocorrelation function.

spec

power spectrum.

croot.ar

characteristic roots of AR operator. See Details.

croot.ma

characteristic roots of MA operator. See Details.

References

Kitagawa, G. (2010) Introduction to Time Series Modeling. Chapman & Hall/CRC.

Aliases
  • armaimp
Examples
# NOT RUN {
# AR model : y(n) = a(1)*y(n-1) + a(2)*y(n-2) + v(n)
a <- c(0.9 * sqrt(3), -0.81)
armaimp(arcoef = a, v = 1.0, n = 1000, lag = 20)

# MA model : y(n) = v(n) - b(1)*v(n-1) - b(2)*v(n-2)
b <- c(0.9 * sqrt(2), -0.81)
armaimp(macoef = b, v = 1.0, n = 1000, lag = 20)

# ARMA model :  y(n) = a(1)*y(n-1) + a(2)*y(n-2)
#                      + v(n) - b(1)*v(n-1) - b(2)*v(n-2)
armaimp(arcoef = a, macoef = b, v = 1.0, n = 1000, lag = 20)
# }
Documentation reproduced from package TSSS, version 1.2.3, License: GPL (>= 2)

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