# Computing the fitted value for the first observation in a time series

Given coefficients from an arima model, how do you calculate the "fitted value" for the first observation of the series?

For example, given the data (called xshort):

and a call to R:

mod<-Arima(xshort,order=c(1,0,0))
mod$coef  it is simple to produce the fitted values. For example the second entry in the series is: mod$coef[1]*xshort[1]+((1-mod$coef[1])*mod$coef[2])

But, how is the first fitted value calculated, which from Arima should be 1038.3884776139?

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