Cointegration, Spread Dynamics, and GARCH-Type Volatility Modeling: An Empirical Econometrics Framework

Abstract

This paper develops a unified methodological framework for studying cointegration, timevarying hedge ratios, and GARCH-type volatility dynamics in mean-reverting financial spreads. When asset prices are integrated of order one, the identification of cointegrated relationships and the estimation of spread dynamics are sensitive to the choice of testing procedure, volatility proxy, and evaluation criterion. Using Monte Carlo simulations together with an illustrative empirical design based on foreign exchange and equity markets, the paper compares EngleGranger and Johansen procedures, static and Kalman-filter-based hedge-ratio estimation, and alternative specifications for modeling conditional heteroskedasticity in the spread residual. The results indicate that model rankings are criterion-dependent: statistical loss functions, economic performance measures, and tail-risk criteria can yield materially different preferred specifications. Model confidence set evidence further suggests that, in finite samples, multiple plausible models may remain empirically indistinguishable. The paper contributes to the econometrics of cointegrated financial systems by integrating spread-volatility modeling, criterion sensitivity, and model uncertainty within a common evaluation framework.

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