Huge technical improvements in data collection and storage are nowadays taking place and allow to form an increasingly accurate picture of many economic phenomena. In order to benefit from such superior data collection, one needs appropriate statistical tools that can help to extract the most important features of the data and turn them into information.
Functional data analysis (FDA) allows to study both cross-sectional and time series data in their original full richness, in addition to traditional methods that usually focus only on a few moments and/or quantiles. For example, in studying earning distribution dynamics, one may use FDA to keep track of the evolution of the whole density function of individual income over time or, when analyzing quantities that are recorded at arbitrarily high frequency (such as e.g. asset prices, interest rates, exchange rates), FDA allows to model and estimate their evolution in continuous time. This motivates the increasingly important role that FDA is recently gaining as a field of research in statistics and econometrics.
The present activity aims at exploring the applicability of FDA, with specific interest to its time series applications. The cooperation with leading European and US experts in the field will contribute to the excellence of the output and to its international outreach.
While members of the research group have experience in time series methods, none of them has already produced research in the area of functional time series analysis.
However, in January 2017 the proponent has visited Prof. Yoosoon Chang and Prof. Joon Park (Indiana University, US), who are leading experts in the field, and has initiated a research collaboration. No other scientific group in Italy is entertaining such an activity, or plans to do so, to the best of the proponent's knowledge.
The proponent has also ongoing research collaborations with Prof. Søren Johansen (Aarhus University and University of Copenhagen, DK) and Prof. Paolo Paruolo (Joint Research Centre of the European Commission, Ispra, IT), who are a leading experts in cointegration analysis of finite dimensional systems.
The research group aims at contributing both to the development and to the application of functional time series analysis. More specifically, one primary aim is to analyze EU income distribution data via functional methods. Until now, no such empirical study has been conducted on European data. One more objective is to explore the possibility of extending econometric methods for functional time series models. This would allow to address, inter alia, the issues of persistence associated with unit root behavior in functional time series.
The overall expected value-added of this activity is both empirical and theoretical. The activity aims at providing key scientific findings for policy decisions, as well as improved technical solutions.
BIBLIOGRAPHY
Franchi, M., and Paruolo, P. (2011) A characterization of vector autoregressive processes with common cyclical features. Journal of Econometrics, 163:105-117.
Franchi, M., and Paruolo, P. (2011) Inversion of regular analytic matrix functions: local Smith form and subspace duality. Linear Algebra and its Applications, 435: 2896-2912.
Franchi, M. (2010) A representation theory for polynomial cofractionality in vector autoregressive models, Econometric Theory, 26: 1201-1217.
Franchi, M. (2007) The integration order of vector autoregressive processes, Econometric Theory 23: 546-553.