mulbar {timsac} | R Documentation |
Determine multivariate autoregressive models by a Bayesian procedure. The basic least squares estimates of the parameters are obtained by the householder transformation.
mulbar(y, max.order=NULL, plot=FALSE)
y |
a multivariate 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. |
plot |
logical. If TRUE daic is plotted. |
The statistic AIC is defined by
AIC = nlog(det(v)) + 2k,
where n is the number of data, v is the estimate of innovation variance matrix, det is the determinant and k is the number of free parameters.
Bayesian weight of the m-th order model is defined by
W(n) = const * C(m) / (m+1),
where const is the normalizing constant and C(m)=exp(-0.5AIC(m)).
The Bayesian estimates of partial autoregression coefficient matrices of forward and backward models are obtained by (m = 1,...,lag)
G(m) = G(m) D(m),
H(m) = H(m) D(m),
where the original G(m) and H(m) are the (conditional) maximum likelihood estimates of the highest order coefficient matrices of forward and backward AR models of order m and D(m) is defined by
D(m) = W(m) + ... + W(lag).
The equivalent number of parameters for the Bayesian model is defined by
ek = (D(1)^2 + ... + D(lag)^2) id + id (id+1)/2
where id denotes dimension of the process.
mean |
mean. |
var |
variance. |
v |
innovation variance. |
aic |
AIC(m), (m = 0,...,max.order). |
aicmin |
minimum AIC. |
daic |
AIC(m)-aicmin (m = 0,...,max.order). |
order.maice |
order of minimum AIC. |
v.maice |
innovation variance attained at m=order.maice. |
bweight |
Bayesian weights. |
integra.bweight |
integrated Bayesian Weights. |
arcoef.for |
AR coefficients (forward model). arcoef.for[i,j,k] shows the value of i-th row, j-th column, k-th order. |
arcoef.back |
AR coefficients (backward model). arcoef.back[i,j,k] shows the value of i-th row, j-th column, k-th order. |
pacoef.for |
partial autoregression coefficients (forward model). |
pacoef.back |
partial autoregression coefficients (backward model). |
v.bay |
innovation variance of the Bayesian model. |
aic.bay |
equivalent AIC of the Bayesian (forward) model. |
H.Akaike (1978) A Bayesian Extension of The Minimum AIC Procedure of Autoregressive Model Fitting. Research Memo. NO.126, The Institute of Statistical Mathematics.
G.Kiagawa 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.
data(Powerplant) z <- mulbar(Powerplant, max.order=10) z$pacoef.for z$pacoef.back