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 2*sqrt(n), where n is the length of the time series y.
plot logical. If TRUE (default) daic, pacoef and pspec are plotted.

Details

The AR model is given by

y(t) = a(1)y(t-1) + .... + a(p)y(t-p) + u(t)

where p is AR order and u(t) is Gaussian white noise with mean 0 and variance v(p).

The basic statistic AIC is defined by

AIC = nlog(det(v)) + 2m,

where n is the length of data, v is the estimate of innovation variance, and m is the order of the model.

Bayesian weight of the m-th order model is defined by

W(m) = CONST*C(m) / (m+1),

where CONST is the normalizing constant and C(m)=exp(-0.5AIC(m)).

The equivalent number of free parameter for the Bayesian model is defined by

ek = D(1)^2 +...+ D(k)^2 +1

where D(j) is defined by D(j)=W(j) +...+ W(k).

m in the definition of AIC is replaced by ek to be define an equivalent AIC for a Bayesian model.

Value

mean mean.
var variance.
v innovation variance.
aic AIC(m) (m = 0,...,ar.order).
aicmin minimum AIC.
daic AIC(m)-aicmin (m = 0,...,ar.order).
order.maice order of minimum AIC.
v.maice innovation variance attained at m=order.maice.
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 Autoregressivemodel 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

[Package timsac version 1.2.1 Index]