TSSS (version 1.2.3)

armaimp: Calculate Characteristics of Scalar ARMA Model

Description

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

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.

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.

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

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)
# }