# How to compute prediction interval if using simple moving average t o predict?

If I want to use simple moving average to make a prediction. For example given h=1 and m=13. $$\hat{x}_{t+1}=\frac{\sum_{j=1}^{13}x_{t-j+1}}{13}$$. What is the prediction interval going to be? How to calculate the half width?

• You need an assumption about how the $x_t$ are generated. If the $x_t$ are iid $N(\mu,\sigma^2)$ then the standard deviation of the forecast $\hat{x}_{t+1}$ is $\sigma/\sqrt{13}$. If the $x_t$ are a random walk without drift i.e. $x_{t+1}=x_t+\epsilon_{t+1}$ where $\epsilon_t \sim N(0,\sigma^2)$ then another formula holds. If the $x_t$ are an AR(1) process, then yet another formula, etc. You have to specify your assumption about $x_t$. Feb 17 '20 at 16:39
• Thanks! Guess you are right! Feb 18 '20 at 2:20