Abstract: The problem of testing a class of double-functional coeffcient ARCH-M models is considered in this paper. An empirical likelihood test based on orthogonal weighting is proposed by constructing an auxiliary random vector with orthogonal weighting. Under some regular conditions, it is theoretically proved that the constructed empirical log-likelihood ratio test statistic asymptotically obeys the chi-square distribution, and the rejection domain with a certain confidence level is obtained, and finally the test effcacy is discussed by numerical simulation.