timsac (version 1.3.8-4)

xsarma: 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)

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.

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.

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