I am studying the ARMA models, and I am breaking my head on something probably straightforward but that I can't see.
I generated in R a simple AR(1) model, and used the function ARIMA to estimate its coefficients. I get two coefficients, an AR(1) coefficient and an intercept.
Now I am trying to calculate myself the fitted values. On another post on StackExchange I found that I can find the fitted value Y(i) by doing
Y(i-1)*model$coef + ((1-model$coef)*model$coef)
Can somebody please explain why one has to multiply the intercept with 1 minus the AR(1) coefficient?
Thanks in advance!
PS This is the other question I was reffering to: Computing the fitted value for the first observation in a time series