New Methods and Theory for the Comparison of Nonparametric Trend Curves

• Applicant: Professor Dr. Michael Vogt
• Subject Area: Statistics and Econometrics
• Term: from 2019 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 430668955

• Final Report Year: 2023

Final Report Abstract

The comparison of time trends is an important topic in time series econometrics. In the project, we have developed multiscale methods for the comparison of nonparametric trend curves. These new methods have crucial advantages over standard approaches: (i) They are effectively free of bandwidth parameters as they take into account multiple bandwidths simultaneously. (ii) They are much more informative: in contrast to most standard methods, they do not only allow to test whether the time trends under consideration are the same or not. They also allow to make confidence statements about which trends are different and where (that is, in which time periods) they differ. They thus provide valuable information for practitioners. The work programme of the project consists of two main parts: the development of (a) multiscale tests and (b) multiscale clustering algorithms. (a) was motivated by the outbreak of the COVID-19 crisis. It concentrates on constructing a multiscale test for the comparison of epidemic time trends. In the empirical part of the paper, the test is applied to detect differences between the time trends of new COVID-19 infections in various European countries. A multiscale test in a general time trend framework was developed which includes covariates and a fixed effect error structure and which is relevant for a wide range of economic applications. The test is complemented by a multiscale clustering algorithm which allows to detect groups of time series with the same trend. The wide applicability of the developed multiscale test and clustering methods is demonstrated by two empirical examples on house prices and GDP growth. All multiscale methods developed in the project are implemented in the R package MSinference which is freely available on CRAN. In addition, the R scripts used to run the simulation exercises and data applications are provided in GitHub repositories, which allows to fully replicate the empirical work carried out in the course of the project.

Publications

• Multiscale comparison of nonparametric trend curves. Revise and Resubmit requested at Journal of Business & Economic Statistics.
  KHISMATULLINA, M. & VOGT, M.
  
• Nonparametric comparison of epidemic time trends: The case of COVID-19. Journal of Econometrics, 232(1), 87-108.
  Khismatullina, Marina & Vogt, Michael