Univariate vs multivariate time series

Univariate time series is one numeric signal indexed by time — daily temperature, hourly request count, monthly revenue. The model gets one value per timestamp and has to forecast the next.

Multivariate time series is several signals indexed by the same time — temperature and humidity and wind speed; request count and error rate and CPU. The model sees a vector at each timestamp.

The confusing part is that "multivariate" gets used for several different shapes. Sometimes it means one target plus external predictors. Sometimes it means many similar target series in a panel. Sometimes it means several endogenous targets forecast jointly. Those are not just storage formats — they imply different modeling assumptions.

The first question is the data shape. The second, more important question is the modeling assumption: do these signals merely help the target, or do they need to be forecast jointly?

Extra signals help when they contain predictive information about the target. Forecasting building energy: outside temperature is a strong driver, so a model with that exogenous variable beats a univariate one. Forecasting stock prices from price + volume + sentiment: the auxiliary signals carry information the price alone doesn't.

Univariate makes sense when the target's own history is the main signal and adding more features mostly adds noise — often the case when the series has strong seasonality and stable structure. ARIMA, Holt-Winters, or per-series neural models can be hard to beat in that regime: once seasonality and lags are captured, the auxiliary signals stop carrying new information.

Panel data is a third shape worth naming: many time series in parallel, one per entity (store, sensor, user). The series may share a timeline or not — that's not what makes panel data different. What makes it different is that each entity has its own target series. The model may learn across entities, but it's not necessarily forecasting one joint vector where every variable is an endogenous target. Panel methods exist because unit-level heterogeneity is now a thing you have to model.

Models to reach for:

• Univariate — one signal forecasting:

  • Classical: ARIMA / SARIMA, Holt-Winters / ETS, Prophet
  • Deep learning: per-series N-BEATS, N-HiTS
  • Foundation (zero-shot): TimesFM (Google), Lag-Llama (open)

• Univariate target with exogenous variables / covariates — one target forecast helped by side-channel inputs:

  • Classical: SARIMAX
  • Deep learning: DeepAR, TFT (Temporal Fusion Transformer — explicit past + future known features), PatchTST, TimesNet, iTransformer, TSMixer
  • Foundation (varying degrees of covariate / multivariate support): Chronos-2 (Amazon), Moirai (Salesforce), TimeGPT (Nixtla)

• Multivariate as joint targets — forecast several related series together:

  • Classical: VAR / VARMA
  • Deep learning: iTransformer (treats variates as tokens), encoder-decoder variants

• Panel — many series in parallel, one per entity:

  • Global neural models: DeepAR, TFT, N-BEATS in global mode
  • Per-entity: fixed-effects regression, hierarchical Bayesian models
  • Foundation via wrapper: Chronos / Chronos-Bolt through AutoGluon-TimeSeries — per-series indexing plus optional exogenous regressors

Full breakdown — shapes, exogenous variables, panel layout, the storage and modeling implications of each: see Time Series Data: Univariate, Multivariate, Panel, and Exogenous Variables.