R: Bayesian Method of Locally Stationary Multivariate AR Model...

blomar {timsac} | R Documentation

## Bayesian Method of Locally Stationary Multivariate AR Model Fitting

### Description

Locally fit multivariate autoregressive models to non-stationary time series by a Bayesian procedure.

### Usage

      blomar(y, max.order = NULL, span)

### 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, `span` is n-m.

### 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 `v`.

### Value

`mean` | mean.
`var` | variance.
`bweight` | Bayesian weight.
`aic` | AIC with respect to the present data.
`arcoef` | AR coefficients. `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.
`eaic` | equivalent AIC of Bayesian model.
`init` | start point of the data fitted to the current model.
`end` | end point of the data fitted to the current 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 (1978) A Bayesian Extension of The Minimum AIC Procedure of Autoregressive Model Fitting. Research Memo. NO.126. The institute of Statistical Mathematics.

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

### Examples

    data(Amerikamaru)
    blomar(Amerikamaru, max.order = 10, span = 300)

[Package timsac version 1.3.6 Index]