Calculation of MA model in R

Question

Trying to manually calculate the fitted values from arima in R in order to understand the model. What I am finding is that even though I have not yet learned to calculate the first p values in a AR(p) or MA(p) model, even when I take values returned from arima the first few fitted values dont seem to match. What am I doing wrong?

R Code:

install.packages("forecast")
library(forecast)

wineindT<-window(wineind, start=c(1987,1), end=c(1994,8))
      write.table(wineindT,"clipboard",sep="\t")
mod3<-Arima(wineindT,order=c(0,0,1))
mod3$coef
       write.table(mod3$coef,"clipboard",sep="\t")
       write.table(forecast.Arima(mod3,1)$fitted,"clipboard",sep="\t")
forecast.Arima(mod3,1)$fitted
mod3$residuals
      write.table(mod3$residuals,"clipboard",sep="\t")

Here is an Excel calculation: Given the first residual (from arima) my calculation is off for series value 2 and 3 then is correct.

Answer 1

This is to do with the definition of a residual. The residuals returned by arima() and Arima() are standardized to have constant variance. So these are not exactly the same as the error values that are used to compute the fitted values. The standardization only affects the first few residuals.

By the way, it is simpler to use fitted(mod3) and residuals(mod3) to calculate the fitted values and the residuals then it is to use your method.

Actually, fitted(mod3) returns wineindT - residuals(mod3) which are not actually the true fitted values. But the difference is small and for most purposes it doesn't matter.