blomar: Bayesian Method of Locally Stationary Multivariate AR Model...

In timsac: Time Series Analysis and Control Package

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)

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.

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.

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)

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