Modelling functional time series, time series of random functions defined within a finite interval, has became one of the main frontiers of developments in time series models. Various functional linear and nonlinear time series models have been proposed and extensively studied in the past two decades (e.g., Bosq, 2000; Hörmann and Kokoszka, 2010; Horváth and Kokoszka, 2012; Hörmann, Horváth and Reeder, 2013; Li, Robinson and Shang, 2020). These models together with relevant methodologies have been applied to various fields such as biology, demography, economics, environmental science and finance. However, the model frameworks and methodologies developed in the aforementioned literature heavily rely on the stationarity assumption, which is often rejected when testing the functional time series data in practice. For example, Horváth, Kokoszka and Rice (2014) find evidence of nonstationarity for intraday price curves of some stocks collected in the US market; Aue, Rice and Sönmez (2018) reject the null hypothesis of stationarity for the temperature curves collected in Australia; and Li, Robinson and Shang (2023) reveal evidence of nonstationary feature for the functional time series constructed from the age-and sex-specific life-table death counts. It thus becomes imperative to test whether the collected functional time series are stationary. The primary interest of this paper is to test whether there exist structural breaks in the mean function over time and subsequently estimate locations of breaks if they do exist. There have been increasing interests on detecting and estimating structural breaks in functional time series. Broadly speaking, there are two types of detection techniques.

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.