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 devided 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-Staionary 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 1.2.1 Index]