A univariate time-series is a sequence of real values
\(\overrightarrow{x}=(x_1,..,x_n )\in{R}^n\)
Similarly, a multivariate time-series is a sequence of real vectors
\(\overrightarrow{X} = (\overrightarrow{x}_1,..,\overrightarrow{x}_n ) \in \mathbb{R}^{n \times k}\)
where $n$ is the maximum length of timestamps, and $k$ is the number of features in the input.
A time-series anomaly detection algorithm that takes as input either $\overrightarrow{x}$ or $\overrightarrow{X}$ and outputs $y\in \left{0,1\right}^n$ such that $y_i=1$ if the $i^{th}$ timestamp is an anomaly.