crossseries

Crossseries is a term used to describe the study of relationships between two or more time series, focusing on how one series relates to another across time, capturing lead-lag effects, co-movements, and potential causal interactions.

In practice, cross-series analysis uses cross-covariance and cross-correlation functions to quantify dependencies at different lags. More advanced models include vector autoregression (VAR), cointegration tests (Johansen, Engle-Granger), and Granger causality to assess directionality. Other approaches include transfer entropy and dynamic conditional correlation in multivariate GARCH frameworks.

Applications of crossseries analysis span several fields. In finance, it is used for pricing, portfolio selection, and risk management across assets. In macroeconomics, it supports forecasting with multiple indicators. In neuroscience, it helps analyze simultaneous neural signals to infer functional connectivity. In climate science, cross-series methods model interdependencies among environmental variables.

Challenges and limitations include non-stationarity and unit roots, which can lead to spurious relationships if not properly addressed. Preprocessing steps such as differencing or testing for cointegration are common. Other practical concerns involve mismatched sampling rates, missing data, noise, and the risk of over-interpretation when multiple tests are performed without correction.

Related concepts include multivariate time series, cross-correlation, cross-covariance, vector autoregression, Granger causality, and cointegration. Crossseries methods are commonly implemented in statistical software and used to uncover temporal dependencies across multiple data streams.