BackcastResidualsAR: Innovation Residuals in AR
In FitAR: Subset AR Model Fitting

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Obtains the residuals (estimated innovations). The residuals for t=1,...,p are obtained using the backforecasting algorithm of Box and Jenkins (1970).

1	BackcastResidualsAR(y, phi, Q = 100, demean=TRUE)

`y`	a time series or vector
`phi`	AR coefficients, lags 1,...,p
`Q`	for backcasting, the AR is approximated by an MA(Q)
`demean`	subtract sample mean

The backforecasting algorithm is described in detail in the book of Box and Jenkins (1970). The idea is to compute the expected value of the innovation assuming a high-order MA(q).

Vector of residuals

No check is done that the AR is causal-stationary.

A.I. McLeod and Y. Zhang

Box and Jenkins (1970). Time Series Analysis: Forecasting and Control.

InvertibleQ, FitAR

#compare residuals obtained using backcasting with fitted parameters and
# the residuals extracted from output of FitAR.  They are identical.
p<-11
out<-FitAR(log(lynx), p)
phi<-out$phiHat #fitted parameters
resphi<-BackcastResidualsAR(log(lynx), phi)
sum(abs(resphi-resid(out)))