The potential relationship between time deformation and generalized autoregressive conditional heteroscedasticity (GARCH) is examined. Despite time deformation and GARCH being mean and variance equation phenomena, respectively, they are argued herein to share a common motivation relating to the examination of changes in the temporal evolution of time‐series processes. Via extensive simulation analysis, a close connection between the two concepts is established. It is found that the presence of GARCH can result in the spurious detection of time deformation, particularly when examining the heavy‐tailed distributions and volatile data typically considered in empirical finance. It is shown that although the application of heteroskedasticity corrected covariance matrix estimators often increases, rather than corrects, the detected oversizing of the tests of time deformation, the application of GARCH filters does provide a solution to size distortion. The findings of the experimental analysis are drawn upon to provide a robust empirical examination of the London housing market where evidence of overwhelming and widespread nonlinearity is detected in the form of time deformation. The implications of these findings for the conduct of future, and the interpretation of previous, research are discussed.