Abstract: In this paper, the Hausman tests are applied to linear GARCH-type error models, with a focus on the LGARCH(1,1) model for simplicity. The specific forms of Hausman tests are given for the LGARCH(1,1) model, and the high-frequency data information is further introduced into these tests. The simulation results show that the Hausman tests perform well for the LGARCH(1,1) model at the daily frequency. Empirical studies based on the SSE 50 Index show that the introduction of intraday high frequency data for Hausman tests can provide more information about the distribution of the error term.