blocar {timsac}

Bayesian Method of Locally Stationary AR Model Fitting; Scalar Case

Description

Locally fit autoregressive models to non-stationary time series by a Bayesian procedure.

Usage

blocar(y, max.order = NULL, span, plot = TRUE)

Arguments

y

a univariate 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.

span

length of basic local span.

plot

logical. If TRUE (default), spectrums pspec are plotted.

Details

The basic AR model of scalar time series y(t) (t=1, \ldots ,n) is given by

y(t) = a(1)y(t-1) + a(2)y(t-2) + \ldots + a(p)y(t-p) + u(t),

where p is order of the model and u(t) is Gaussian white noise with mean 0 and variance v. At each stage of modeling of locally AR model, a two-step Bayesian procedure is applied

1.	Averaging of the models with different orders fitted to the newly obtained data.
2.	Averaging of the models fitted to the present and preceding spans.

AIC of the model fitted to the new span is defined by

AIC = ns \log( sd ) + 2k,

where ns is the length of new data, sd is innovation variance and k is the equivalent number of parameters, defined as the sum of squares of the Bayesian weights. AIC of the model fitted to the preceding spans are defined by

AIC( j+1 ) = ns \log( sd(j) ) + 2,

where sd(j) is the prediction error variance by the model fitted to j periods former span.

Value

var

variance.

aic

AIC.

bweight

Bayesian weight.

pacoef

partial autocorrelation.

arcoef

coefficients ( average by the Bayesian weights ).

v

innovation variance.

init

initial point of the data fitted to the current model.

end

end point of the data fitted to the current model.

pspec

power spectrum.

References

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 (1978) A Bayesian Extension of the Minimum AIC Procedure of Autoregressive Model Fitting. Research Memo. NO.126. The Institute of The Statistical Mathematics.

H.Akaike, G.Kitagawa, E.Arahata and F.Tada (1979) Computer Science Monograph, No.11, Timsac78. The Institute of Statistical Mathematics.

Examples

data(locarData)
z <- blocar(locarData, max.order = 10, span = 300)
z$arcoef