Rejoinder to the discussion of “An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models”

Abstract

Let us first of all thank the Editors for organizing such a wide, deep and interesting discussion, and the authoritative scientists who accepted to give their contribution. We are particularly proud that Professor Tong participated the discussion, since he is the father of the threshold principle, and also the first proposal of a nonlinear nonstationary threshold model is due to him. A first general suggestion is to widen the proposed analysis, taking into account at least monthly data for analyzing seasonality, as so convincingly argued by Professor Bohm, and spatial relationships possibly integrating a dynamic cluster analysis. This is undoubtedly a crucial point, and calls for further study. Moreover, the present paper is essentially a statistical analysis based on a particular model, by no means exhaustive, while a deeper study would require a more specific climate knowledge. We are particularly honored that two authoritative climatologists accepted to read our paper and to contribute this discussion, and hope this may be an occasion for future fruitful collaboration. A second general question, as raised by Professor Piccolo, is more delicate and concerns the concept of data generating process, and the extent a model should try to reproduce it rather than privileging fitting. This is a controversial issue: we reported Rissanen’s position, Professor Tong cites the famous Box’s dictum all models are wrong but some are useful, Professor Piccolo’s position seems partially different. Such an important issue, dating back at least to themeasurement without theory debate (Koopmans 1947), cannot be appropriately discussed here; we just confirm that our