R: Minimum AIC Method of Locally Stationary AR Model Fitting;...

mlocar {timsac} | R Documentation

## Minimum AIC Method of Locally Stationary AR Model Fitting; Scalar Case

### Description

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

### Usage

      mlocar(y, max.order = NULL, span, const = 0, plot = TRUE)

### Arguments

`y` | a univariate time series.
`max.order` | upper limit of the order of AR model. Default is 2*sqrt(n), where n is the length of the time series `y`.
`span` | length of the basic local span.
`const` | integer. `0` denotes constant vector is not included as a regressor and `1` denotes constant vector is included as the first regressor.
`plot` | logical. If `TRUE` (default), spectrums `pspec` are plotted.

### Details

The data of length n are divided into k locally stationary spans,

|<-- n1 -->|<-- n2 -->|<-- n3 -->| ..... |<-- nk -->|

where ni (i=1,...,k) denotes the number of basic spans, each of length span, which constitute the i-th locally stationary span. At each local span, the process is represented by a stationary autoregressive model.

### Value

`mean` | mean.
`var` | variance.
`ns` | the number of local spans.
`order` | order of the current model.
`arcoef` | AR coefficients of current model.
`v` | innovation variance of the current model.
`init` | initial point of the data fitted to the current model.
`end` | end point of the data fitted to the current model.
`pspec` | power spectrum.
`npre` | data length of the preceding stationary block.
`nnew` | data length of the new block.
`order.mov` | order of the moving model.
`v.mov` | innovation variance of the moving model.
`aic.mov` | AIC of the moving model.
`order.const` | order of the constant model.
`v.const` | innovation variance of the constant model.
`aic.const` | AIC of the constant model.

### References

G.Kitagawa and H.Akaike (1978) A Procedure for The Modeling of Non-Stationary Time Series. Ann. Inst. Statist. Math., 30, B, 351–363.

H.Akaike, G.Kitagawa, E.Arahata and F.Tada (1979) Computer Science Monograph, No.11, Timsac78. The Institute of Statistical Mathematics.

### Examples

    data(locarData)
    z <- mlocar(locarData, max.order = 10, span = 300, const = 0)
    z$arcoef

[Package timsac version 1.3.6 Index]