Linear vs. threshold cointegration approaches to price discovery: The case of the Warsaw Stock Exchange

Abstract

This study evaluates and compares the usefulness of the classical Vector Error Correction Model (VECM) and the Threshold Vector Error Correction Model (TVECM) in analyzing the price discovery process on the Warsaw Stock Exchange. The empirical analysis uses daily data on the WIG20 index and its futures contracts from 2018 to 2024. The VECM results indicate unidirectional long-run and short-run causality from the spot market to the futures market, with the latter primarily adjusting to deviations from equilibrium. The estimated common factor weights suggest that the spot market accounts for about two-thirds of the overall price discovery. Based on these findings alone, one might conclude that the dominance of the spot market is stable and persistent. However, the TVECM reveals substantial nonlinearities and regime-dependent dynamics that challenge this conclusion. It identifies three regimes, corresponding to undervaluation, near-equilibrium, and overvaluation of futures, within which the adjustment mechanisms differ notably. In both the lower and middle regimes, the error correction mechanism is weak or statistically insignificant, indicating that deviations from equilibrium are not systematically eliminated. In particular, the middle regime, which accounts for the majority of observations, can be interpreted as a no-arbitrage band in which mispricing is too small to trigger arbitrage activity. In the upper regime, although both markets respond to deviations, their adjustments occur in the same direction, preventing the restoration of equilibrium and suggesting a breakdown of the classical arbitrage mechanism. This behavior may reflect the presence of common informational shocks and heightened market uncertainty rather than a stable lead–lag relationship between the markets. The comparison demonstrates that while the VECM provides a convenient summary of average relationships, it oversimplifies the underlying dynamics by assuming a constant adjustment process. The TVECM offers a more informative framework by capturing regime-specific behavior and revealing that the price discovery process is unstable, asymmetric, and sensitive to market conditions. These findings highlight the importance of nonlinear approaches in analyzing financial market dynamics, particularly in periods of increased volatility.