Provide an automatic ARMA model fitting procedure.
Models with various orders are fitted and the best choice is determined with
the aid of
the statistics AIC.
Usage
autoarmafit(y, max.order = NULL)
Value
best.model
the best choice of ARMA coefficients.
model
a list with components arcoef (Maximum likelihood
estimates of AR coefficients), macoef (Maximum likelihood estimates
of MA coefficients), arstd (AR standard deviation), mastd
(MA standard deviation), v (Innovation variance), aic
(AIC \(= n \log(det(v))+2(p+q)\)) and grad
(Final gradient) in AIC increasing order.
Arguments
y
a univariate time series.
max.order
upper limit of AR order and MA order. Default is
\(2 \sqrt{n}\), where \(n\) is the length of the time series
y.
Details
The maximum likelihood estimates of the coefficients of a scalar ARMA model
$$y(t) - a(1)y(t-1) -...- a(p)y(t-p) = u(t) - b(1)u(t-1) -...- b(q)u(t-q)$$
of a time series \(y(t)\) are obtained by using DAVIDON's variance algorithm.
Where \(p\) is AR order, \(q\) is MA order and \(u(t)\) is a zero mean
white noise. Pure autoregression is not allowed.
References
H.Akaike, E.Arahata and T.Ozaki (1975) Computer Science Monograph, No.5,
Timsac74, A Time Series Analysis and Control Program Package (1).
The Institute of Statistical Mathematics.
# "arima.sim" is a function in "stats".# Note that the sign of MA coefficient is opposite from that in "timsac".y <- arima.sim(list(order=c(2,0,1),ar=c(0.64,-0.8),ma=-0.5), n = 1000)
autoarmafit(y)