A coarse-mesh projection method has been developed for the Monte Carlo calculation of dominant eigenvalue ratio [dominance ratio (DR)]. The first step of the method consists of the regression analysis of the multivariate time series from the coarse-mesh binning of the Monte Carlo fission source distribution. The second step is computation of the eigenvectors of the adjoint matrix of noise propagation. In general, projections on these eigenvectors can be utilized to compute important characteristics of the eigenmodes of fission source distribution. In this work, it has been proven that if the eigenvector corresponding to the largest eigenvalue of the aforementioned adjoint matrix is taken to be the vector for projection, the projected scalar time series follows the autoregressive process of order one with the root of characteristic polynomial, i.e., the autocorrelation coefficient, being the DR of fission source distribution. Numerical results are presented for four problems including one-energy-group checkerboard-type problems, a one-energy-group cube problem and a continuous-energy pressurized water reactor core problem. The strength of the method is twofold; (a) the elimination of the use of autoregressive moving average fitting, and (b) no need to optimize the order of fitting.