R: Non-stationary Power Spectrum Analysis

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 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 = nlog(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)

[Package timsac version 1.3.6 Index]