This paper presents an optimum combination of two robust statistical techniques that can be used to improve the skill of long-range weather forecasts. The first method uses decomposition and analysis based on EEOF (Extended Empirical Orthogonal Functions), with a 3-month data window, for temperature and precipitation fields in Romania. Using Rule N to select the significant components led to 3 modes for temperature and to 9 modes for precipitation. In linear extrapolation, an AR model is used to produce forecast the time series of the EEOF components. The parameters of this model are determined by a method consistent with the maximum entropy method, which is why this model is named AR-MEM. In order to select model order, 7 criteria are tested, some of which are efficient, while the others are consistent. The skill of these methods is tested using simulated time series. Model parameters are determined from observational data over the period 1950 – 1990. The Heidke skill score is computed using independent data (1991-1997). The best 2-month forecasts, (compared to persistence) were obtained using the EEOF 3 temperature component. Better results have been obtained for the temperature field filtered by the first 3 EEOF modes, for the meteorological stations situated in the central part of Romania. For precipitation, the forecast based on the EEOF 1 component with one-step ahead, led to skill scores worse than those obtained using persistence in all cases.