# armaimp

0th

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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.

• 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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