I am quite new to the R and the ARIMA model, and I have a question on the ARIMA model that I obtained in R.

I will use the US unemployment rate as an example, the data range is from Jan, 1948 to Feb, 2015, total of 806 observations. After looking at the AICc, I decided to use ARIMA(2,1,2) model. (BTW I am using Arima() function from "forecast" package in R)

The output is the following:

```
Series: log.unemp
ARIMA(2,1,2)

ar1 1.6406
ar2 -0.7499
ma1 -1.5943
ma2 0.7893

sigma^2 estimated as 0.001307: log likelihood=1530.14
AIC=‐3050.27 AICc=‐3050.2 BIC=‐3026.82

```

The code is 

```
fit.best <- Arima(log.unemp, c(2, 1, 2), include.constant=FALSE)
print(fit.best)

```

Then I want to measure the forecast performance of this model. That is, to calculate things like RMSE, Theil's U, etc. But I do not know how to do that. The reason is that it seems that I do not know how to derive the forecast equation from this output to calculate the fitted values.

So could anyone help me on this? How should I derive the forecast equation from this output? Also, after obtaining the equation, how can I do the forecast in Excel to calculate the fitted values from the first data point (there are some numbers that are not available when you are calculating the fitted value for `t=1`)?

Thanks!