nonst {timsac}

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 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.

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.

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)