fit.ar.par {partsm} | R Documentation |
This function fits either an autoregressive (AR) or a periodic autoregressive (PAR) model and extract the estimates for the autoregressive or periodic autoregressive coefficients.
fit.ar.par (wts, type, detcomp, p)
wts |
a univariate time series object. |
type |
A character string indicating whether the model to fit is an autoregressive model,
"AR" , or a periodic autoregressive model, "PAR" . |
detcomp |
deterministic components to include in the model. Three types of regressors can be
included: regular deterministic components, seasonal deterministic components, and any regressor
variable previously defined by the user.
This argument must be a list object with the following elements: regular=c(0,0,0) ,
if the first and second element are set equal to 1, it indicates that an intercept, and/or linear trend,
respectively, are included. The third element in regular is a vector indicating which seasonal
dummies should be included. If no seasonal dummies are desired it must be set equal to zero. For
example, regular=c(1,0,c(1,2,3)) would include an intercept, no trend, and the first three
seasonal dummies;
seasonal=c(0,0) , if an element is set equal to 1, it indicates that seasonal intercepts, and/or
seasonal trends, respectively, are included in the model;
regvar=0 , if none regressor variables are considered, this object must be set equal to zero,
otherwise, the names of a matrix object previously defined should be indicated. |
p |
the lag order of the model. |
If type
is "AR"
the following model is estimated by ordinary least squares:
y_t = phi_{1} y_{t-1} + phi_{2} y_{t-2} + ... + phi_{p} y_{t-p} + ε_t.
If type
is "PAR"
, the following model is estimated by ordinary least squares:
y_t = α_{1s} y_{t-1} + α_{2s} y_{t-2} + ... + α_{ps} y_{t-p} + ε_t,
for s=1,...,S, where S
is the periodicity of the time series.
Deterministic components can be added to models above. Be careful when defining the detcomp
argument. To include an intercept and seasonal intercepts, or a regular trend with seasonal trends, will
cause multicollinearity problems.
A fit.partsm-class
class object reporting the estimates of the autoregressive or periodic
autoregressive coefficients. See fit.partsm-class
to check further information available
from this class via the methods show
and summary
.
Javier López-de-Lacalle javlacalle@yahoo.es.
P.H. Franses: Periodicity and Stochastic Trends in Economic Time Series (Oxford University Press, 1996).
fit.piartsm-class
, fit.partsm-class
, and PAR.MVrepr-methods
.
## Models for the the logarithms of the Real GNP in Germany. data("gergnp") lgergnp <- log(gergnp, base=exp(1)) ## Fit an AR(4) model with intercept and seasonal dummies. detcomp <- list(regular=c(1,0,c(1,2,3)), seasonal=c(0,0), regvar=0) out.ar <- fit.ar.par(wts=lgergnp, type="AR", detcomp=detcomp, p=4) ## Fit a PAR(2) model with seasonal intercepts. detcomp <- list(regular=c(0,0,0), seasonal=c(1,0), regvar=0) out.par <- fit.ar.par(wts=lgergnp, type="PAR", detcomp=detcomp, p=2)