Time Series Modelling

Time series consist of data observed sequentially in time, and they are assumed to stem from an underlying stochastic process. The scope of time series approaches thus covers models for stochastic processes as well as inferential procedures for model fitting, model diagnostics, forecasting, and various other applications.
While time series data have been collected for a relatively long time in history (one may recall the famous time series on sunspot numbers), the development of methods and stochastic models for such time series is more recent. Indeed, one of the motivations for announcing the Special Issue in 2020 was the fact that this year can be considered a twofold ’anniversary year’ of time series modeling. On the one hand, the correlogram, the autoregressive (AR), and the moving-average (MA) models for time series, all of which are nowadays part of any course on time series analysis and covered by any statistical software, date back to the 1920s (mainly driven by G. U. Yule, G. T. Walker, and E. E. Slutzky; see Nie and Wu [1] for a detailed discussion). On the other hand, the first comprehensive textbook on time series was published by Box and Jenkins [2] in 1970, so 2020 allowed the celebration of both the semi-centennial and centennial anniversary at the same time.