R: Univariate Bayesian Method of AR Model Fitting

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.
`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

[Package timsac version 1.3.6 Index]