In this paper, we propose a unified approach to generating standardized-residuals-based correlation tests for checking GARCH-type models. This approach is valid in the presence of estimation uncertainty, is robust to various standardized error distributions, and is applicable to testing various types of misspecifications. By using this approach, we also propose a class of power-transformed-series (PTS) correlation tests that provides certain robustifications and power extensions to the Box-Pierce, McLeod-Li, Li-Mak, and Berkes-Horváth-Kokoszka tests in diagnosing GARCH-type models. Our simulation and empirical example show that the PTS correlation tests outperform these existing autocorrelation tests in financial time series analysis.