timsac (version 1.3.8-4)

blomar: Bayesian Method of Locally Stationary Multivariate AR Model Fitting

Description

Locally fit multivariate autoregressive models to non-stationary time series by a Bayesian procedure.

Usage

blomar(y, max.order = NULL, span)

Value

mean

mean.

var

variance.

bweight

Bayesian weight.

aic

AIC with respect to the present data.

arcoef

AR coefficients. 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.

eaic

equivalent AIC of Bayesian model.

init

start point of the data fitted to the current model.

end

end point of the data fitted to the current 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 \(2md\), span is \(n-m\).

Details

The basic AR model is given by $$y(t) = A(1)y(t-1) + A(2)y(t-2) + \ldots + A(p)y(t-p) + u(t),$$ where \(p\) is order of the AR model and \(u(t)\) is innovation variance v.

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 (1978) A Bayesian Extension of The Minimum AIC Procedure of Autoregressive Model Fitting. Research Memo. NO.126. The institute of Statistical Mathematics.

H.Akaike, G.Kitagawa, E.Arahata and F.Tada (1979) Computer Science Monograph, No.11, Timsac78. The Institute of Statistical Mathematics.

Examples

data(Amerikamaru)
blomar(Amerikamaru, max.order = 10, span = 300)