timsac (version 1.3.8)

mlocar: 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)

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.

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,

$$|<-- n_1 -->|<-- n_2 -->|<-- n_3 -->| ..... |<-- n_k -->|$$

where \(n_i\) (\(i=1,\ldots,k\)) 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.

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