Multivariate Time Series
A multivariate time series tracks several variables over time that may influence each other, such as temperature, humidity, and energy demand. Modeling them together can beat treating each alone.
Why model jointly
- One series can act as a leading indicator for another, like rising orders before rising shipments.
- Shared shocks, such as a holiday, move many series at once.
- A joint model captures these cross effects that single series methods miss.
Classic and modern tools
- A vector autoregression predicts each variable from recent past values of all variables, capturing linear cross dependence.
- Neural sequence models like recurrent networks or temporal transformers learn nonlinear interactions across many inputs.
Causation caution
A model that uses other series as inputs assumes those inputs are known or forecastable at prediction time. If a driver variable is itself unknown in the future, you must forecast it too or treat it carefully. Correlation between series does not prove causation, so a useful predictor may not be a true cause.
Key idea
Multivariate forecasting models several interacting series jointly to capture cross effects, while staying honest about future inputs and causation.