timsac (version 1.3.0)

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)

Arguments

y

a univariate time series.

arcoefi

initial estimates of AR coefficients.

macoefi

initial estimates of MA coefficients.

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.

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