blocar {timsac} | R Documentation |
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
|
span |
length of basic local span. |
plot |
logical. If |
Details
The basic AR model of scalar time series is given by
where is order of the model and
is Gaussian white noise
with mean
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
where is the length of new data,
is innovation variance
and
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
where is the prediction error variance by the model fitted to
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