There are many different types of time series forecasting tasks. Forecasting tasks can be categorized by different criteria. For example, we can categorize them by the number of variables in the series and their relations to each other.

In the introduction of this chapter, we already discussed some terminologies of time series forecasting. In this section, we dive deep into the details of univariate time series forecasting and multivariate time series forecasting.

## Forecasting Univariate Time Series¶

In a univariate time series forecasting task, we are given a single time series and asked to forecast future steps of the series.

Given a time series $$\{y_{t}\}$$, we train a model to forecast $$\color{red}y_{t+1:t+H}$$ using input $$\color{blue}y_{t-K:t}$$, i.e., we build a model $$f$$ such that

$f({\color{blue}y_{t-K:t}}) \to {\color{red}y_{t+1:t+H}}.$

## Forecasting Multivariate Time Series¶

In a multivariate time series forecasting task, we will deal with multiple time series. Naively, we expect multivariate time series forecasting to be nothing special but adding more series. However, the complication comes from the fact that different series may not be aligned well at all time steps.

In the introduction of this chapter, we have shown the basic ideas of targets $$\mathbf y$$ and covariates $$\mathbf x$$ and $$\mathbf u$$. In the following illustration, we expand the idea to the multivariate case.

Contributors: LM