> [!tldr] > If $(X_{t})$ is a time series, then the process of **prewhitening** transforms it into something close to white noise. It facilitates the analysis and interpretation of many time series techniques. For example, if we model $X_{t}=f(t, X_{t-1},\dots)+\epsilon_{t}$ where $\epsilon_{t}$ is an additive, independent noise, then we can estimate $f$ with some $\hat{f}$, and transform $X_{t}\mapsto X_{t}-\hat{f}(t,X_{t-1},\dots)$ to get a prewhitened series.