Fully modified least absolute devotions and fully modified M in estimating regression model with non-stationary explanatory variable and auto correlated random errors

The research is concerned with the adoption of two robust estimation methods: The fully modified least absolute devotions method (FM-LAD) and the fully modified M method (FM-M), in estimating the parameters of regression model with non-stationary explanatory variable and autocorrelated random errors which can be modeled according to one of the mixed models, autoregressive and moving average (ARMA). The research aims to make a comparison between these two methods based on the results of their estimation using simulation experiments prepared for this purpose. The results of the simulation experiment showed the advantage of the fully modified M method over the second method depending on the trade-off criterion mean squared error (MSE).