mlomar: Minimum AIC Method of Locally Stationary Multivariate AR...

In timsac: Time Series Analysis and Control Package

Minimum AIC Method of Locally 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, 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+const, span is n-m.
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 divided into k locally stationary spans,

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

where n_i (i=1,\ldots,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)

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