What is the difference between univariate and multivariate time series?

A univariate time series consists of a single variable measured over time, while a multivariate time series involves two or more variables measured over the same time intervals. The key distinction lies in the number of variables and how they interact. Univariate data focuses on understanding patterns, trends, or forecasts for one metric, such as daily temperature readings. Multivariate data, by contrast, explores relationships between multiple variables, such as temperature, humidity, and wind speed recorded simultaneously. This difference impacts how the data is modeled, analyzed, and interpreted.

From a technical perspective, univariate time series are represented as a sequence of values indexed by time, like a 1D array [y₁, y₂, ..., yₙ] where each yₜ is a single observation. For example, a developer working with stock prices might track closing prices each day as a univariate series. Multivariate time series, however, are structured as a matrix or 2D array where each row contains multiple measurements at a given timestamp. For instance, a sensor dataset with columns like [temperature, pressure, vibration] sampled hourly would be multivariate. When preprocessing data, developers often reshape multivariate series into a format compatible with models (e.g., [samples, timesteps, features] in deep learning frameworks like TensorFlow).

The choice between univariate and multivariate approaches depends on the problem. Univariate models, such as ARIMA or Exponential Smoothing, are simpler and faster to implement but ignore external factors. Multivariate models, like VAR (Vector Autoregression) or LSTM networks with multiple input features, can capture dependencies between variables. For example, predicting energy demand might require both historical demand and weather data (multivariate), whereas forecasting a single product’s sales could use univariate data. Developers must weigh trade-offs: multivariate models often need more data, computational resources, and careful feature selection to avoid overfitting, but they can provide deeper insights when variables influence each other.