This tutorial talks about the exponential smoothing and forecasts based on it.

### 1 Objective and Assumptions

Given a past history \(\{x_1,x_2,\cdots,x_n\}\Longrightarrow\)we want to predict some future value \(x_{n+k}\).

We assume that:

- We assume there is no systematic trend or seasonal effects in the process, or that these have been identified and removed.
- The mean of the process can change from one time step to the next, but we have no information about the likely direction of these changes.