R: Exact Maximum Likelihood Method of Scalar ARMA Model Fitting

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 1.3.6 Index]