partsm (version 1.0-1)

fit.ar.par: Fit an Autoregressive or Periodic Autoregressive Model

Description

This function fits either an autoregressive (AR) or a periodic autoregressive (PAR) model and extract the estimates for the autoregressive or periodic autoregressive coefficients.

Usage

fit.ar.par (wts, type, detcomp, p)

Arguments

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 m

p

the lag order of the model.

Value

• 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.

Details

If type is "AR" the following model is estimated by ordinary least squares:

$$y_t = \phi_{1} y_{t-1} + \phi_{2} y_{t-2} + ... + \phi_{p} y_{t-p} + \epsilon_t.$$ If type is "PAR", the following model is estimated by ordinary least squares:

$$y_t = \alpha_{1s} y_{t-1} + \alpha_{2s} y_{t-2} + ... + \alpha_{ps} y_{t-p} + \epsilon_t,$$

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.

References

P.H. Franses: Periodicity and Stochastic Trends in Economic Time Series (Oxford University Press, 1996).

See Also

fit.piartsm-class, fit.partsm-class, and PAR.MVrepr-methods.

Examples

## 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)