timsac (version 1.3.8-4)

mlomar: 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)

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.

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.

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)