unibar {timsac} | R Documentation |
Univariate Bayesian Method of AR Model Fitting
Description
This program fits an autoregressive model by a Bayesian procedure. The least squares estimates of the parameters are obtained by the householder transformation.
Usage
unibar(y, ar.order = NULL, plot = TRUE)
Arguments
y |
a univariate time series. |
ar.order |
order of the AR model. Default is
|
plot |
logical. If |
Details
The AR model is given by
where is AR order and
is Gaussian white noise with mean
and variance
. The basic statistic AIC is defined by
where is the length of data,
is the estimate of innovation
variance, and
is the order of the model.
Bayesian weight of the -th order model is defined by
where is the normalizing constant and
. The equivalent number of
free parameter for the Bayesian model is defined by
where is defined by
.
in the definition of AIC is replaced by
to be define an
equivalent AIC for a Bayesian model.
Value
mean |
mean. |
var |
variance. |
v |
innovation variance. |
aic |
AIC. |
aicmin |
minimum AIC. |
daic |
AIC- |
order.maice |
order of minimum AIC. |
v.maice |
innovation variance attained at m= |
pacoef |
partial autocorrelation coefficients (least squares estimate). |
bweight |
Bayesian Weight. |
integra.bweight |
integrated Bayesian weights. |
v.bay |
innovation variance of Bayesian model. |
aic.bay |
AIC of Bayesian model. |
np |
equivalent number of parameters. |
pacoef.bay |
partial autocorrelation coefficients of Bayesian model. |
arcoef |
AR coefficients of Bayesian model. |
pspec |
power spectrum. |
References
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.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(Canadianlynx)
z <- unibar(Canadianlynx, ar.order = 20)
z$arcoef