TSSS (version 1.3.1)

armachar: Calculate Characteristics of Scalar ARMA Model

Description

Calculate impulse response function, autocovariance function, autocorrelation function and characteristic roots of given scalar ARMA model.

Usage

armachar(arcoef = NULL, macoef = NULL, v, lag = 50, nf = 200, plot = TRUE, ...)

Value

An object of class "arma" which has a plot method. This is a list with components:

impuls

impulse response function.

acov

autocovariance function.

parcor

PARCOR.

spec

power spectrum.

croot.ar

characteristic roots of AR operator. See Details.

croot.ma

characteristic roots of MA operator. See Details.

Arguments

arcoef

AR coefficients.

macoef

MA coefficients.

v

innovation variance.

lag

maximum lag of autocovariance function.

nf

number of frequencies in evaluating spectrum.

plot

logical. If TRUE (default), impulse response function, autocovariance, power spectrum, PARCOR and characteristic roots are plotted.

...

graphical arguments passed to the plot method.

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

References

Kitagawa, G. (2020) Introduction to Time Series Modeling with Applications in R. Chapman & Hall/CRC.

Examples

# AR model : y(n) = a(1)*y(n-1) + a(2)*y(n-2) + v(n)
a <- c(0.9 * sqrt(3), -0.81)
armachar(arcoef = a, v = 1.0, 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)
armachar(macoef = b, v = 1.0, 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)
armachar(arcoef = a, macoef = b, v = 1.0, lag = 20)