Generated synthetic time series aim to be both realistic by mirroring the characteristics of real-world time series and useful by including characteristics that are useful for subsequent applications, such as forecasting and missing value imputation. To generate such realistic and useful time series, we require generation methods capable of controlling the non-stationarity and periodicities of the generated time series. However, existing approaches do not consider such explicit control. Therefore, in the present paper, we present a novel approach to control non-stationarity and periodicities with calendar and statistical information when generating time series. We first define the requirements for methods to generate time series with non-stationarity and periodicities, which we show are not fulfilled by existing generation methods. Second, we formally describe the novel approach for controlling non-stationarity and periodicities in generated time series. Thirdly, we introduce an exemplary implementation of this approach using a conditional Invertible Neural Network (cINN). We evaluate this cINN empirically in experiments with real-world data sets and compare it to state-of-the-art time series generation methods. Our experiments show that the evaluated cINN can generate time series with controlled periodicities and non-stationarity, and it also generally outperforms the selected benchmarks.

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Model diagnostics and forecast evaluation are closely related tasks, with the former concerning in-sample goodness (or lack) of fit and the latter addressing predictive performance out-of-sample. We review the ubiquitous setting in which forecasts are cast in the form of quantiles or quantile-bounded prediction intervals. We distinguish unconditional calibration, which corresponds to classical coverage criteria, from the stronger notion of conditional calibration, as can be visualized in quantile reliability diagrams. Consistent scoring functions—including, but not limited to, the widely used asymmetric piecewise linear score or pinball loss—provide for comparative assessment and ranking, and link to the coefficient of determination and skill scores. We illustrate the use of these tools on Engel's food expenditure data, the Global Energy Forecasting Competition 2014, and the US COVID-19 Forecast Hub. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 10 is March 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Time series forecasting is fundamental for various use cases in different domains such as energy systems and economics. Creating a forecasting model for a specific use case requires an iterative and complex design process. The typical design process includes five sections (1) data preprocessing, (2) feature engineering, (3) hyperparameter optimization, (4) forecasting method selection, and (5) forecast ensembling, which are commonly organized in a pipeline structure. One promising approach to handle the ever‐growing demand for time series forecasts is automating this design process. The article, thus, reviews existing literature on automated time series forecasting pipelines and analyzes how the design process of forecasting models is currently automated. Thereby, we consider both automated machine learning (AutoML) and automated statistical forecasting methods in a single forecasting pipeline. For this purpose, we first present and compare the identified automation methods for each pipeline section. Second, we analyze these automation methods regarding their interaction, combination, and coverage of the five pipeline sections. For both, we discuss the reviewed literature that contributes toward automating the design process, identify problems, give recommendations, and suggest future research. This review reveals that the majority of the reviewed literature only covers two or three of the five pipeline sections. We conclude that future research has to holistically consider the automation of the forecasting pipeline to enable the large‐scale application of time series forecasting. This article is categorized under: Technologies > Machine Learning Technologies > Prediction Algorithmic Development > Spatial and Temporal Data Mining

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