Misleading dynamics: The erosion of Durbin-Watson power through time aggregation

This paper investigates the impact of temporal aggregation on the ability of the Durbin-Watson (DW) test to detect first-order autocorrelation. Through Monte Carlo simulations for AR(1), AR(2), and ARMA(1,1) processes, it demonstrates that the power function of the DW test significantly diminishes when data are aggregated from daily to weekly or monthly frequencies, especially when using arithmetic averaging. Even minor autocorrelation becomes increasingly difficult to detect, with the DW statistic converging to 2.0 under smoothing. An empirical analysis of 6,647 daily USD/EUR and USD/GBP exchange rate observations from 1999 to 2025 confirms the simulation results: DW statistics tend to be close to 2.0 at all levels of aggregation in the presence of underlying volatility. Temporal aggregation also reduces volatility and normalizes distributional characteristics, further obscuring residual dynamics. These findings highlight the risk of obtaining spurious negatives in autocorrelation testing when using the DW test on aggregated data and suggest more reliable diagnostics in applied econometrics.