ADF Unit Root Test - Engel-Granger Test Implementation

The Engel-Granger test, commonly implemented as the ADF (Augmented Dickey-Fuller) unit root test, is a fundamental statistical procedure for detecting unit roots in time series data. This econometric technique is crucial for determining time series stationarity and analyzing long-term trends and patterns. In MATLAB, the Engel-Granger test can be efficiently implemented using the Econometrics Toolbox through functions like `adftest()` for unit root testing and `egcitest()` for cointegration analysis. The implementation typically involves: - Preprocessing time series data using `timetable` or `table` arrays - Applying `adftest()` with appropriate lag selection criteria (AIC/BIC) to test individual series for unit roots - Utilizing `egcitest()` to examine cointegration relationships between non-stationary variables - Configuring test parameters including trend specification, significance levels, and residual diagnostics Key algorithmic considerations include handling deterministic trends (constant, linear, or both) and selecting optimal lag lengths using information criteria. The MATLAB implementation provides comprehensive output including test statistics, p-values, and critical values, enabling robust statistical inference. Additional functionality allows for residual analysis, model specification testing, and visualization of cointegration relationships. This integrated approach enables researchers to perform sophisticated time series analysis, identify structural relationships, and validate econometric models through rigorous statistical testing, leading to more accurate forecasting and economic insights.