FitARLS(FitAR) | R Documentation |
The usual subset AR model is defined by selecting a subset of the AR coefficients and setting all other coefficients to zero. Usually this subset model is fit using least squares.
FitARLS(z, p, SubsetQ = FALSE, lag.max = "default")
z |
time series |
p |
Vector specifying which lags to use in the AR. If SubsetQ=FALSE, p should be a scalar and a regular AR(p) will be fit. For p=0, white noise. |
SubsetQ |
default FALSE. Ignored if p has length > 1. Need set to TRUE for ambiguous cases – see Note. |
lag.max |
The maximum lag to be used in the Portmanteau Test |
The design matrix, X, is formed by concatenating together the needed columns and then the R function lsfit is used. An intercept term is used with lsfit. The residuals are computed using BackcastResidualsAR. The exact loglikelihood is computed using LoglikelihoodAR.
A list with class name "FitAR" and components:
loglikelihood |
value of the loglikelihood using LoglikelihoodAR |
phiHat |
coefficients in AR(p) – including 0's |
sigsqHat |
innovation variance estimate |
muHat |
estimate of the mean |
covHat |
covariance matrix of the coefficient estimates |
zetaHat |
transformed parameters, length(zetaHat)=# coefficients estimated |
RacfMatrix |
residual autocorrelations and sd for lags 1...lag.max |
LjungBox |
table of Ljung-Box portmanteau test statistics |
SubsetQ |
parameters in AR(p) – including 0's |
res |
innovation residuals, same length as z |
fits |
fitted values, same length as z |
SubsetQ |
parameters in AR(p) – including 0's |
lags |
lags used in AR model |
demean |
TRUE if mean estimated otherwise assumed zero |
FitMethod |
"LS" for this function |
tsp |
tsp(z) |
call |
result from match.call() showing how the function was called |
yX |
the dependent variable column prepended to the columns of independent variables |
ModelTitle |
description of model |
DataTitle |
returns attr(z,"title") |
If SubsetQ=FALSE, this is equivalent to the built-in function ar( ..., method="OLS"). Note that least-squares residuals are not used. The residuals are calculated using BackcastResidualsAR and the loglikelihood is calculated using LoglikelihoodAR.
A.I. McLeod
Tong, H. (1977). Some comments on the Canadian lynx data. Journal of the Royal Statistical Society A 140, 432-436.
FitAR
,
LoglikelihoodAR
,
BackcastResidualsAR
,
ar
#Compare the fit achieved by the two types of subset models z<-log(lynx) pvec<-SelectModel(z, SubsetModel="z", method="BIC", lag.max=12, Best=1) pvec FitARLS(z, pvec) FitAR(z, pvec)