Robust Inference on Correlation under General Heterogeneity

Considerable evidence in past research shows size distortion in standard tests for zero autocorrelation or cross-correlation when time series are not independent identically dis-tributed random variables, pointing to the need for more robust procedures. Recent tests for serial correlation and cross correlation in Dalla, Giraitis, and Phillips (2022) provide a more robust approach, allowing for heteroskedasticity and dependence in un-correlated data under restrictions that require a smooth, slowly-evolving deterministic heteroskedasticity process. The present work removes those restrictions and validates the robust testing methodology for a wider class of heteroskedastic time series models and innovations. The updated analysis given here enables more extensive use of the method-ology in practical applications. Monte Carlo experiments conÞrm excellent Þnite sample performance of the robust test procedures even for extremely complex white noise pro-cesses. The empirical examples show that use of robust testing methods can materially reduce spurious evidence of correlations found by standard testing procedures.