timsac (version 1.3.0)

nonst: 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.

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.

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.

Examples

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