nonst {timsac}R Documentation

Non-stationary Power Spectrum Analysis

Description

Locally fit autoregressive models to non-stationary time series by AIC criterion.

Usage

nonst(y, span, max.order = NULL, plot = TRUE)

Arguments

y

a univariate time series.

span

length of the basic local span.

max.order

highest order of AR model. Default is 2n2 \sqrt{n}, where nn 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(t1)+A(2)y(t2)+...+A(p)y(tp)+u(t),y(t) = A(1)y(t-1) + A(2)y(t-2) +...+ A(p)y(t-p) + u(t),

where pp is order of the AR model and u(t)u(t) is innovation variance. AIC is defined by

AIC=nlog(det(sd))+2k,AIC = n \log(det(sd)) + 2k,

where nn is the length of data, sdsd is the estimates of the innovation variance and kk is the number of parameter.

Value

ns

the number of local spans.

arcoef

AR coefficients.

v

innovation variance.

aic

AIC.

daic21

= AIC2 - AIC1.

daic

= daic21/n/n (nn 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.

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.

Examples

# Non-stationary Test Data
data(nonstData)
nonst(nonstData, span = 700, max.order = 49)

[Package timsac version 1.3.8-4 Index]