unibar: Univariate Bayesian Method of AR Model Fitting

In timsac: Time Series Analysis and Control Package

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) + \ldots + 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 = n\log(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 \times \frac{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 + \ldots + D(k)^2 +1,

where D(j) is defined by D(j)=W(j) + \ldots + 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.
aicmin	minimum AIC.
daic	AIC-aicmin.
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 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

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