mlocar: Minimum AIC Method of Locally Stationary AR Model Fitting;...

In timsac: Time Series Analysis and Control Package

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 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.

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-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

timsac documentation built on Sept. 30, 2023, 5:06 p.m.