Distribution of AR1 coefficient
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