Cointegration
Cointegration identifies a stationary long-run combination of nonstationary time series and supports error-correction analysis in finance and economics.
Correlation, covariance, regression, time-series, and cointegration methods for measuring financial relationships without overstating what the data prove.
Correlation, Regression, and Time Series covers statistical methods used to measure co-movement, estimate conditional relationships, model chronological dependence, and test proposed long-run links in financial data.
Start with the question rather than the most sophisticated method. Correlation standardizes linear co-movement, while Covariance retains scale and enters portfolio-risk calculations directly.
Regression Analysis estimates conditional relationships. Time Series Analysis addresses ordering, persistence, seasonality, and forecasting. Cointegration is the narrower framework for stable combinations of integrated nonstationary series.
| Question | Start with | Do not conclude automatically |
|---|---|---|
| How strongly do two return series move together? | Correlation | That one causes the other or the relationship is stable |
| How does joint variation enter portfolio risk? | Covariance | That a historical covariance matrix covers stress conditions |
| How is an outcome conditionally related to one or more variables? | Regression | That the estimated coefficient is causal or forecasts well |
| How do trend, seasonality, lags, or changing volatility affect a series? | Time-series analysis | That a historical pattern will continue |
| Do nonstationary levels share a stable linear combination? | Cointegration | That deviations create risk-free or profitable trades |
Return to Statistical Relationships and Time-Series Analysis for aggregation, quantiles, and moving-average methods.
This section provides general financial and statistical education. It does not provide a forecast, trading signal, model validation, or personalized investment, legal, tax, or accounting advice.
Choose a subsection first. Deeper term pages live inside each subsection, which keeps large topic hubs readable.
Cointegration identifies a stationary long-run combination of nonstationary time series and supports error-correction analysis in finance and economics.
Correlation standardizes the linear co-movement between two variables and helps analysts assess diversification, factor exposure, and changing financial relationships.
Covariance measures joint variation between two variables and supplies the cross-asset terms used in portfolio risk and factor models.
Regression analysis estimates conditional relationships between financial variables and helps explain returns, test drivers, forecast outcomes, and quantify uncertainty.
Time series analysis examines financial observations in chronological order to model trend, seasonality, persistence, volatility, and forecast uncertainty.