This project is a continuation of the research line initiated by the Principal Investigator of this project, Luis Alberiko Gil Alaña, in 2002 in relation to the theoretical models of long memory and fractional integration and their empirical extension linked to the analysis of poverty. The project has two parts: one theoretical and another one practical. 

Regarding the theoretical part of the project, the fractional integration or I(d) models will be extended to various forms of nonlinearity including both deterministic and stochastic methods in the study of aspects such as the possible asymmetry of shocks in time series, investigating whether the effects of the shocks have a permanent or transitory nature. 

These issues will be examined not only in the usual I(d) models, where the pole or singularity in the spectral density function occurs at zero frequency, but also in those models where such singularity occurs at a frequency far from zero, which allows us to study cases such as fractional stationarity or singular or multiple fractional cyclicity. The possibility of multiple poles or singularities in the spectrum will also be investigated in the present project, as well as other forms of nonlinearity such as neural networks, Fourier transforms, wavelets and quadratic and cubic components in fractional integration contexts.

From an empirical point of view, the standard fractional integration models together with the new models developed in this project will be employed in different disciplines, using time series data including areas such as Economics and Finance, Energy, Environment, Climatology and Meteorology, Tourism, Development Economics, Inequality or Urbanism together with the study of the influence that COVID-19 may have had on this type of time series.

This project has a duration of three years: from 2021 to 2023. 

Proyecto PID2020-113691-RB-I00 financiado por MCIN/ AEI /10.13039/501100011033