Complex exponential smoothing

Exponential smoothing has been one of the most popular forecasting methods usedto support various decisions in organizations, in activities such as inventory man-agement, scheduling, revenue management, and other areas. Although its relativesimplicity and transparency have made it very attractive for research and practice,identifying the underlying trend remains challenging with significant impact on theresulting accuracy. This has resulted in the development of various modifications oftrend models, introducing a model selection problem. With the aim of addressingthis problem, we propose the complex exponential smoothing (CES), based on thetheory of functions of complex variables. The basic CES approach involves only twoparameters and does not require a model selection procedure. Despite these simpli-fications, CES proves to be competitive with, or even superior to existing methods.We show that CES has several advantages over conventional exponential smooth-ing models: it can model and forecast both stationary and non-stationary processes,and CES can capture both level and trend cases, as defined in the conventionalexponential smoothing classification. CES is evaluated on several forecasting com-petition datasets, demonstrating better performance than established benchmarks.We conclude that CES has desirable features for time series modeling and opens newpromising avenues for research.CC BY 4.0Attribution 4.0 InternationalFirst published: 02 August 2022Correspondence: Ivan Svetunkov, Centre for Marketing Analytics and Forecasting, Lancaster University Management School, Lancaster, Lancashire, LA1 4YX, UK. Email: i.svetunkov@lancaster.ac.uk