FORECASTING Model AR(1) in an Autoregressive Form The Pi´s Parameters

Ive been implementing a little exercise to obtain the first 2 forecasting points of an AR(1) process. And i want to have the forecasting ponts using the three forms: Im folowing this pdf http://www.le.ac.uk/users/dsgp1/COURSES/BANKERS/BANKERS6.PDF

Difference Equation Forms, Moving Aerage Form and Auroregressive Form:

I did well for the first two forms:

library(forecast)
set.seed(20141221)
x <- arima.sim(n=108, list(ar=0.5))
data.ts <- ts(x, start=c(1999,01), freq=12)
time = window(data.ts, start=c(1999,01),end=c(2007,12))
inflarima1 <- arima( x,order = c(1, 0, 0))

inflarima1$coef # ar1 intercept #0.4945659 0.2069526 predict(inflarima,2)$pred
#Jan       Feb
#2008 0.1147776 0.1613660


FIRST FORM: Difference Equation Form

# c^= INTERCEPT*(1-phi)
#h=1 -> yt+1 = c^ + phi*Yt
0.2069526*(1-0.4945659) + 0.4945659*x[108]
0.1147776
#h=2 -> yt+1 = c^ + phi*Yt+1 = c^ + phi*[c^ + phi*Yt]= c^+phi*c^+ phi^2*Yt
0.2069526*(1-0.4945659) + 0.2069526*(1-0.4945659)*0.4945659
+ 0.4945659^2*x[108]
0.1613660


SECOND FORM: MOVING AVERAGE

#Forecasting h=1;

#Yt+h = mu + phi*et + phi^(2)*et-1 +... + phi^(108)*et-107