Nonstationarity and cointegration emerged as the central paradigm in time series econometrics, linking unit-root behavior with long-run equilibrium via error-correction representations and shared estimation challenges across autoregressive systems. Multivariate time series modeling matured into unified vector autoregressive frameworks, systems of simultaneous equations, and likelihood-based estimation, enabling consistent inference on cross-equation dynamics and long-run relationships. Diagnostics and specification testing advanced, with portmanteau-type measures and model adequacy procedures guiding empirical specification; nonlinear and bilinear extensions broadened the linear ARMA toolkit to capture regime-dependent dynamics. Influential Works: Distribution of the Estimators for Autoregressive Time Series with a Unit Root established the foundations for nonstationary inference and the Dickey-Fuller framework. Specification Tests in Econometrics provided a general misspecification testing framework with local power results, influencing model validation and robustness across applied work. Cointegration and Error-Correction: Representation, Estimation, and Testing formalized how long-run relationships could be represented and tested in multivariate time series, while ARCH models introduced time-varying volatility and spurred subsequent volatility modeling.