The autoregressive conditional heteroscedasticity (ARCH) model and its various generalizations have been widely used to analyze economic and financial data. Although many variables like GDP, inflation and commodity prices are imprecisely measured, the problem of measurement error in ARCH-type models has not been studied in the literature. We study an ARCH model where the underlying process is subject to additive measurement error and show that the model is identifiable by using the observations of the proxy process. We propose GMM estimators for unknown parameters and a hypothesis test for the presence of measurement error. We study the impact of measurement error on the naive maximum likelihood estimators and the finite sample performance of the proposed estimators using Monte Carlo simulations. This is a joint work with Mustafa Salamh.