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Exponential smoothing in state space form (ETS) is a popular forecasting technique, widely used in research and practice. While the additive error ETS models have been well studied, the multiplicative error ones have received much less attention in forecasting literature. Still, these models can be useful in cases, when one deals with positive data, because they are supposed to work in such situations. Unfortunately, the classical assumption of normality for the error term might break this property and lead to non-positive forecasts on positive data. In order to address this issue we propose using Log-Normal, Gamma and Inverse Gaussian distributions, which are defined for positive values only. We demonstrate what happens with ETS(M,*,*) models in this case, discuss conditional moments of ETS with these distribution and show that they are more natural for the models than the Normal one. We conduct the simulation experiments in order to study the bias introduced by point forecasts in these models and then compare the models with different distributions. We finish the paper with an example of application, showing how pure multiplicative ETS with a positive distribution works.

Forecasting and Analytics with the Augmented Dynamic Adaptive Model (ADAM) focuses on a time series model in Single Source of Error state space form, called “ADAM” (Augmented Dynamic Adaptive Model). The book demonstrates a holistic view to forecasting and time series analysis using dynamic models, explaining how a variety of instruments can be used to solve real life problems. At the moment, there is no other tool in R or Python that would be able to model both intermittent and regular demand, would support both ETS and ARIMA, work with explanatory variables, be able to deal with multiple seasonalities (e.g. for hourly demand data) and have a support for automatic selection of orders, components and variables and provide tools for diagnostics and further improvement of the estimated model. ADAM can do all of that in one and the same framework. Given the rising interest in forecasting, ADAM, being able to do all those things, is a useful tool for data scientists, business analysts and machine learning experts who work with time series, as well as any researchers working in the area of dynamic models.

Many modern statistical models are used for both insight and prediction when applied to data. When models are used for prediction one should optimise parameters through a prediction error loss function. Estimation methods based on multiple steps ahead forecast errors have been shown to lead to more robust and less biased estimates of parameters. However, a plausible explanation of why this is the case is lacking. In this paper, we provide this explanation, showing that the main benefit of these estimators is in a shrinkage effect, happening in univariate models naturally. However, this can introduce a series of limitations, due to overly aggressive shrinkage. We discuss the predictive likelihoods related to the multistep estimators and demonstrate what their usage implies to time series models. To overcome the limitations of the existing multiple steps estimators, we propose the Geometric Trace Mean Squared Error, demonstrating its advantages. We conduct a simulation experiment showing how the estimators behave with different sample sizes and forecast horizons. Finally, we carry out an empirical evaluation on real data, demonstrating the performance and advantages of the estimators. Given that the underlying process to be modelled is often unknown, we conclude that the shrinkage achieved by the GTMSE is a competitive alternative to conventional ones.