Modeling functional time series with dynamic factor structures and points of impact

• Applicant: Dr. Sven Otto
• Subject Area: Statistics and Econometrics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 511905296

Many econometric time series are governed by a smooth functional structure, as in the case of energy spot prices, income profiles, age distributions, or the term structure of bond yields and credit default swaps. The development of methods for analyzing functional data has primarily been focused on independent curve observations. Models for time-dependent functional data studied in the literature so far are based on simple frameworks such as functional autoregressions or function on function regressions with one regressor. Economic applications, however, often require more complex modeling frameworks than a simple functional regression, while the complex estimation approaches of traditional functional data methods discourage applied econometricians from using these methods. The aim of this project is to further develop estimation and inferential methods for functional time series relevant to empirical economic research. The conventional functional autoregressive modeling approach is complemented by dynamic factor structures and points of impact. Additional points of impact allow for complex dependence structures, and factor models provide a convenient, user-friendly modeling framework popular among economists. Identifying these generalized models poses further technical issues, which will be addressed in detail in this project. In particular, the operator in the general functional autoregressive model with a concurrent point of impact belongs to a larger class than that of the Hilbert-Schmidt regression operators. If the (auto)correlation relationship can be explained by a low-dimensional factor structure, the identification of the operator becomes more straightforward and can be obtained by imposing suitable conditions on the idiosyncratic component. The estimators proposed for these modeling variants are based on (dynamic) functional principal components. Their asymptotic properties and tools for statistical inference will be analyzed in detail. Moreover, hypothesis tests for testing and monitoring the structural stability will be developed. Applications to financial and energy-economic data shall demonstrate the practical usefulness of the methods in estimation and forecasting exercises, and software packages will be created to be readily usable for practitioners.

• DFG Programme: Research Grants
• International Connection: Spain
• Cooperation Partner: Professor Dr. Nazarii Salish