Ivan was supervised by Dr Nikos Kourentzes and Professor Robert Fildes. The viva was examined by Prof Siem Jan Koopman, a leading authority on state-space modelling and Dr Rebecca Killick from the Statistic Department. During his PhD, Ivan proposed a new forecasting model, the Complex Exponential Smoothing (CES). One of the motivating ideas behind CES is that recent research has demonstrated that the standard forms of exponential smoothing may not be able to capture all the patterns observed in real time series. In particular, the interpretation of the classical level and trend components can be elusive, leading to potential modelling complications. Instead, CES avoids this separation, and introduces a new flexible component that captures various types of information, beyond the level component, as necessary to achieve good fit to the given data.

Ivan looked into the properties of the basic CES model, deriving likelihood, parameter bounds and variance expressions. He then proceeded to extend the model to the seasonal case. He showed that only these two models (non-seasonal and seasonal CES) were adequate to typical types of time series considered within the exponential smoothing framework.

Naturally, there is no global dominance of CES over ETS, but the empirical results are favourable to CES, especially when the qualitative elements of the comparison (simplified or no model selection) are considered. Detailed results are described in two papers, currently under review. Meanwhile there are two presentations by Ivan that you may find helpful about ‌CES and seasonal CES.

Mathematical details about the model can be found in this working paper and an implementation of CES is available in the smooth package for R. A further illustration on forecasting with Complex Exponential Smoothing can be found on Nikos Kourentzes Blog.

Ivan will continue to be part of the LCF as a Post-Doctoral Researcher and the LCF congratulates Ivan on his achievement!