In economics and many other forecasting domains, the real world problems are too complex for a single model that assumes a specific data generation process. The forecasting performance of different methods changesChange(s) depending on the nature of the time series. When forecasting large collections of time series, two lines of approaches have been developed using time series features, namely feature-based model selection and feature-based model combination. This chapter discusses the state-of-the-art feature-based methods, with reference to open-source software implementationsImplementation.

This article considers a bilinear model that includes two different latent effects. The first effect has a direct influence on the response variable, whereas the second latent effect is assumed to first influence other latent variables, which in turn affect the response variable. In this article, latent variables are modelled via rank restrictions on unknown mean parameters and the models which are used are often referred to as reduced rank regression models. This article presents a likelihood-based approach that results in explicit estimators. In our model, the latent variables act as covariates that we know exist, but their direct influence is unknown and will therefore not be considered in detail. One example is if we observe hundreds of weather variables, but we cannot say which or how these variables affect plant growth.

Smooth mixtures, i.e. mixture models with covariate-dependent mixing weights, are very useful flexible models for conditional densities. Previous work shows that using too simple mixture components for modeling heteroscedastic and/or heavy tailed data can give a poor fit, even with a large number of components. This paper explores how well a smooth mixture of symmetric components can capture skewed data. Simulations and applications on real data show that including covariate-dependent skewness in the components can lead to substantially improved performance on skewed data, often using a much smaller number of components. Furthermore, variable selection is effective in removing unnecessary covariates in the skewness, which means that there is little loss in allowing for skewness in the components when the data are actually symmetric. We also introduce smooth mixtures of gamma and log-normal components to model positively-valued response variables.