xsarma: Exact Maximum Likelihood Method of Scalar ARMA Model Fitting

In timsac: Time Series Analysis and Control Package

Exact Maximum Likelihood Method of Scalar ARMA Model Fitting

Description

Produce exact maximum likelihood estimates of the parameters of a scalar ARMA model.

Usage

  xsarma(y, arcoefi, macoefi)

Arguments

y	a univariate time series.
arcoefi	initial estimates of AR coefficients.
macoefi	initial estimates of MA coefficients.

Details

The ARMA model is given by

y(t) - a(1)y(t-1) - \ldots - 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

gradi	initial gradient.
lkhoodi	initial (-2)log likelihood.
arcoef	final estimates of AR coefficients.
macoef	final estimates of MA coefficients.
grad	final gradient.
alph.ar	final ALPH (AR part) at subroutine ARCHCK.
alph.ma	final ALPH (MA part) at subroutine ARCHCK.
lkhood	final (-2)log likelihood.
wnoise.var	white noise variance.

References

H.Akaike (1978) Covariance matrix computation of the state variable of a stationary Gaussian process. Research Memo. No.139. The Institute of Statistical Mathematics.

H.Akaike, G.Kitagawa, E.Arahata and F.Tada (1979) Computer Science Monograph, No.11, Timsac78. The Institute of Statistical Mathematics.

Examples

# "arima.sim" is a function in "stats".
# Note that the sign of MA coefficient is opposite from that in "timsac".
arcoef <- c(1.45, -0.9)
macoef <- c(-0.5)
y <- arima.sim(list(order=c(2,0,1), ar=arcoef, ma=macoef), n = 100)
arcoefi <- c(1.5, -0.8)
macoefi <- c(0.0)
z <- xsarma(y, arcoefi, macoefi)
z$arcoef
z$macoef

timsac documentation built on Sept. 30, 2023, 5:06 p.m.