In this paper, a method of artificial neural networks (NN) is proposed as an alternative tool for the one-step-ahead prediction of composite indicators (CIs) of Lithuania’s economy. CI is composed of widely used social and economic indicators. The NN is applied for forecasting CI during the financial crisis and later periods (2008–2010) on the basis of data of earlier years (1998–2007). In this work, the Extreme Learning Machine (ELM) algorithm is combined with locally weighted regression. The analysis shows that the prediction error of a testing sample is statistically smaller compared to Levenberg–Marquardt or ELM methods.