Robust estimation in time series

Abstract

The main purpose of this work is to study empirically by means of simulations, the robustness of a set of proposals to estimate the parameters in the MA(1) time series model. The non-normal populations are mixtures of normal distributions, defined by g(x) = pN(0, k) + (1 − p)N(0, 1), where the proportion of contamination most frequently used is p = 0.10 and k is the variance of the distribution used in the contamination; α is taken to be 0.90, which is close to the region of non-invertibility. Key results are that the estimation procedures used in the study provide good results in terms of biases in the estimation of the parameters, and that the biases are not changed when contaminated errors (mixtures) are considered. The estimation of the variance of the contaminated errors is also studied through simulations.