Locally fit autoregressive models to non-stationary time series by AIC
criterion.
Usage
nonst(y, span, max.order = NULL, plot = TRUE)
Value
ns
the number of local spans.
arcoef
AR coefficients.
v
innovation variance.
aic
AIC.
daic21
= AIC2 - AIC1.
daic
= daic21\(/n\) (\(n\) is the length of the current
model).
init
start point of the data fitted to the current model.
end
end point of the data fitted to the current model.
pspec
power spectrum.
Arguments
y
a univariate time series.
span
length of the basic local span.
max.order
highest order of AR model. Default is
\(2 \sqrt{n}\), where \(n\) is the length of the time series
y.
plot
logical. If TRUE (the default), spectrums are plotted.
Details
The basic AR model is given by
$$y(t) = A(1)y(t-1) + A(2)y(t-2) +...+ A(p)y(t-p) + u(t),$$
where \(p\) is order of the AR model and \(u(t)\) is innovation variance.
AIC is defined by
$$AIC = n \log(det(sd)) + 2k,$$
where \(n\) is the length of data, \(sd\) is the estimates of the
innovation variance and \(k\) is the number of parameter.
References
H.Akaike, E.Arahata and T.Ozaki (1976) Computer Science Monograph, No.6,
Timsac74 A Time Series Analysis and Control Program Package (2).
The Institute of Statistical Mathematics.