mlomar {timsac}R Documentation

Minimum AIC Method of Loccally 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. Default is 2*sqrt(n), where n is the length of the time series y.
span length of 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.

Details

The data of length n are devided 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 1.2.1 Index]