R: Minimum AIC Method of Locally Stationary Multivariate AR...

mlomar {timsac} | R Documentation

## Minimum AIC Method of Locally Stationary Multivariate AR Model Fitting

### Description

Locally fit multivariate autoregressive models to non-stationary time series by the minimum AIC procedure using the householder transformation.

### Usage

      mlomar(y, max.order = NULL, span, const = 0)

### Arguments

`y` | a multivariate time series.
`max.order` | upper limit of the order of AR model, less than or equal to n/2d where n is the length and d is the dimension of the time series `y`. Default is min(2*sqrt(n), n/2d).
`span` | length of basic local span. Let m denote `max.order`, if n-m-1 is less than or equal to `span` or n-m-1-`span` is less than 2md+`const`, `span` is n-m.
`const` | integer. '0' denotes constant vector is not included as a regressor and '1' denotes constant vector is included as the first regressor.

### Details

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

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

where ni (i=1,...,k) denoted 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.
`aic` | AIC of the current model.
`arcoef` | AR coefficient matrices of the current model. `arcoef[[m]][i,j,k]` shows the value of i-th row, j-th column, k-th order of m-th 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.
`npre` | data length of the preceding stationary block.
`nnew` | data length of the new block.
`order.mov` | order of the moving model.
`aic.mov` | AIC of the moving model.
`order.const` | order 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(Amerikamaru)
    mlomar(Amerikamaru, max.order = 10, span = 300, const = 0)

[Package timsac version 1.3.6 Index]