xsarma {timsac}R Documentation

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) - ... - 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

[Package timsac version 1.2.1 Index]