Forecasting is prevalent. Tourism industry forecasts the number of tourists (Athanasopoulos, Hyndman, Song and Wu, 2011). Energy industry forecasts the demand and price of energy (Raviv, Bouwman and van Dijk, 2013). Finance industry forecasts the prices for crude oil, grain, currency and securities (Asai, Caporin and McAleer, 2012). Policy makers make their decisions based on economic forecasts (Amisano and Geweke, 2013). One of the most widespread forecasting tools is the Box-Jenkins (Box and Jenkins, 1970) autoregressive integrated moving average (ARIMA) model. However, Box-Jenkins methodology has its drawbacks. First, a modern forecaster is faced with lots of potentially useful data which ARIMA models cannot handle. Second, in many areas of forecasting, e.g. in economics, data are noisy. Thus, forecasting methods should be used that are robust against the noise. Third, data dynamics may be subject to sudden change. The forecasting methods should be able to forecast robustly during such changes in dynamics. The increasing demand for forecasting methods that would be able to handle potentially large sets of data subject to noise and changes in dynamics makes the topic of the thesis pertinent. The main objective of the thesis thus is to develop robust forecasting methods that are able to work with noisy and high-dimensional data, with application to macroeconomics. The key novelties of the thesis are the following. First, an asymmetric filter has been developed for frequency band extraction at the end-points of univariate series. Second, a method has been developed for signal extraction and forecasting using high-dimensional and noisy data sets. Third, robustness issues of Bayesian and factor forecasting models have been investigated when the dynamics of the target change rapidly. The approbation of the thesis has been achieved by presenting the results at 11 international scientific conferences and seminars, by publishing 11 articles in international scientific journals or conference proceedings, by implementing the methods at the Central statistical bureau of Latvia and the Bank of Latvia. The thesis consists of an introduction, three chapters and conclusions. It contains 136 pages, 69 figures, 9 tables and 92 references.