Optimal forecasting accuracy using Lp-norm combination

A well-known result in statistics is that a linear combination of two-point forecasts has a smaller Mean Square Error (MSE) than the two competing forecasts themselves (Bates and Granger in J Oper Res Soc 20(4):451–468, 1969). The only case in which no improvements are possible is when one of the single forecasts is already the optimal one in terms of MSE. The kinds of combination methods are various, ranging from the simple average (SA) to more robust methods such as the one based on median or Trimmed Average (TA) or Least Absolute Deviations or optimization techniques (Stock and Watson in J Forecast 23(6):405–430, 2004). Standard regression-based combination approaches may fail to get a realistic result if the forecasts show high collinearity in several situations or the data distribution is not Gaussian. Therefore, we propose a forecast combination method based on Lp-norm estimators. These estimators are based on the Generalized Error Distribution, which is a generalization of the Gaussian distribution, and they can be used to solve the cases of multicollinearity and non-Gaussianity. In order to demonstrate the potential of Lp-norms, we conducted a simulated and an empirical study, comparing its performance with other standard-regression combination approaches. We carried out the simulation study with different values of the autoregressive parameter, by alternating heteroskedasticity and homoskedasticity. On the other hand, the real data application is based on the daily Bitfinex historical series of bitcoins (2014–2020) and the 25 historical series relating to companies included in the Dow Jonson, were subsequently considered. We showed that, by combining different GARCH and the ARIMA models, assuming both Gaussian and non-Gaussian distributions, the Lp-norm scheme improves the forecasting accuracy with respect to other regression-based combination procedures.

Evaluation of a program for promoting physical activity and well-being: Friuli Venezia Giulia in Movimento

This article presents an evaluation of the “Friuli Venezia Giulia in Movimento” project, aimed at promoting the culture of movement and well-being in a region which is particularly affected by population ageing. The goals of the project reside in promoting appropriate lifestyles through the endorsement of healthy behaviours (physical activity, healthy nutrition, well-being); increasing the number of physically active people in the various municipal territories, by enhancing or creating new pedestrian paths that reflect the 10,000-step goal; enhancing the local territory by promoting the existing paths and the initiatives already in place; promoting new paths and environments conducive to physical activity for people of all ages; encouraging the creation of new “walking groups” and the adhesion of people to them to promote physical activity and socialisation, with the consequent improvement of psychophysical well-being. Although the evaluation is still on-going, the preliminary results—obtained by means of two surveys and a multilevel model—show that the initial steps of the project have been carried out satisfactorily and that Municipalities still need to be supported in order to achieve good participation on part of the citizens.

Missing value or behaviour: how to increase the signal of social media data

Social media has become a widespread element of people’s everyday life, which is used to communicate and generate contents. Among the several ways to express a reaction to social media contents, the “Likes” are critical. Indeed, they convey preferences, which drive existing markets or allow the creation of new ones. Nevertheless, the appreciation indicators have some complex features, as for example the interpretation of the absence of “Likes”. In this case, the lack of approval may be considered as a specific behaviour. The present study aimed to define whether the absence of Likes may indicate the presence of a specific behaviour through the contextualization of the treatment of missing data applied to real cases. We provided a practical strategy for extracting more knowledge from social media data, whose synthesis raises several measurement problems. We proposed an approach based on the disambiguation of missing data in two modalities: “Dislike” and “Nothing”. Finally, a data pre-processing technique was suggested to increase the signal of social media data.