Some Basic Examples of Time Series

White noise

Simply put, white noise is a time series with 0 mean, some variance, $\sigma^2$, and 0 autocovariance. More formally, we would say that a series $y_t$ is white noise if $E(y_t) = 0$ and $\sigma^2 \neq0$ for all time steps $k$.

A white noise process would be denoted as $y_t \sim \text{WN}(\sigma^2)$. More often than not, however, we will find white noise represented with Greek letter $\epsilon_t$, so that $\epsilon_t \sim \text{WN}(\sigma^2)$.

That was a lot of mathematical notation, so let’s get more visual. Run the code snippet below.