This dissertation considers the estimation of the parameters of ARMA and GARCH processes by the Minimum Distance Estimator (MOE). The estimator is obtained by minimizing a quadratic distance function between the sample autocorrelation and theoretical autocorrelation functions and has the advantage of imposing very little in terms of distributional assumptions on the innovation process. The asymptotic properties of the MOE for ARMA processes are discussed. The exact asymptotic efficiency of using a block of sample autocorrelations is derived for some low order MA and ARMA models. The MOE is surprisingly efficient for some parts of the parameter space. We also investigate the properties of the MOE when used to estimate linear GARCH models using autocorrelations of the squared process. Monte Carlo results show that the MDE performs better than Quasi-MLE with certain conditional densities which exhibit extreme departures from conditional Gaussianity. An application of the MOE to estimate a GARCH(l, 1) model from high frequency exchange rate data is provided.