Purpose
If the true model is an ar model , then what is the distribution of the ar coefficient ?

> set.seed(1977)
> results <- data.frame()
> phi <- 0.8
> for (i in 1:1000) {
+     x <- arima.sim(n = 100, model = list(ar = phi))
+     y <- as.vector(x)
+     results <- rbind(results, coef(lm(y[2:100] ~ y[1:99] + 0)))
+ }
> as.vector(sd(sqrt(100) * (results - phi)))
[1] 0.6178951

So, you can estimate the distribution of phi - phi(orig) It is a Normal Distribution with mean 0 and variance (1-phi^2)/T