Publications

A) Published Papers 

1) Carpita, M., De Luca, G., Metulini, R., Zuccolotto, P. (2024). Traffic flows time series in a flood-prone area: modeling and clustering on extreme values with a spatial constraint. Stochastic Environmental Research and Risk Assessment, Vol. 38, pp. 3109–3125. doi: 10.1007/s00477-024-02735-x 

Link: https://link.springer.com/article/10.1007/s00477-024-02735-x

Abstract

Time series of traffic flows, extracted from mobile phone origin-destination data, are employed for monitoring people crowding and mobility in areas subject to flooding risk. By applying a vector autoregressive model with exogenous covariates combined with dynamic harmonic regression to such time series, we detected the presence of many extreme events in the residuals, which exhibit heavy-tailed distribution. For this reason, we propose a time series clustering procedure based on tail dependence which is suitable for data characterized by a spatial dimension, since objects' geographical proximity is taken into account. The final aim is to obtain clusters of areas characterized by the common tendency to the manifestation of extreme events, that in this case study are represented by extremely high incoming traffic flows. The proposed method is applied to the Mandolossa, a strongly urbanized area located on the western outskirts of Brescia (northern Italy) which is subject to frequent flooding.

2) Biancalani, F., Gnecco, G., Metulini, R., Riccaboni, M. (2024) The Impact of the European Union Emissions Trading System on Carbon Dioxide Emissions: A Matrix Completion Analysis. Scientific Reports, 14, 19676. doi: 10.1038/s41598-024-70260-6

Link: https://www.nature.com/articles/s41598-024-70260-6#citeas

Abstract

Despite the negative externalities on the environment and human health, today’s economies still produce excessive carbon dioxide emissions. As a result, governments are trying to shift production and consumption to more sustainable models that reduce the environmental impact of carbon dioxide emissions. The European Union, in particular, has implemented an innovative policy to reduce carbon dioxide emissions by creating a market for emission rights, the emissions trading system. The objective of this paper is to perform a counterfactual analysis to measure the impact of the emissions trading system on the reduction of carbon dioxide emissions. For this purpose, a recently-developed statistical machine learning method called matrix completion with fixed effects estimation is used and compared to traditional econometric techniques. We apply matrix completion with fixed effects estimation to the prediction of missing counterfactual entries of a carbon dioxide emissions matrix whose elements (indexed row-wise by country and column-wise by year) represent emissions without the emissions trading system for country-year pairs. The results obtained, confirmed by robust diagnostic tests, show a significant effect of the emissions trading system on the reduction of carbon dioxide emissions: the majority of European Union countries included in our analysis reduced their total carbon dioxide emissions (associated with selected industries) by about 15.4% during the emissions trading system treatment period 2005–2020, compared to the total carbon dioxide emissions (associated with the same industries) that would have been achieved in the absence of the emissions trading system policy. Finally, several managerial/practical implications of the study are discussed, together with its possible extensions.

3) Guerini, S.S., Metulini, R., Forecasting traffic flow time series with Vine-Transform ARMA Copula models, ”Quality & Quantity”, doi: 10.1007/s11135-025-02558-0 

Link: https://rdcu.be/e1UOz

Abstract

Traffic–flow forecasting is gaining prominence in urban areas to facilitate urban planning for early warning systems and optimized logistics. Hence, there is a growing need for simple and high–performing statistical models. This study leverages the Vine–Transform AutoRegressive Moving–Average (VT–ARMA) copula model to forecast traffic data, and it emphasizes the evaluation of forecasting performance. Accordingly, we used real–life data on origin–destination signals extracted from mobile phone signals for specific areas in the province of Brescia (Italy). We conducted performance evaluation using the rank–graduation box approach along with a moving window cross–validation strategy, and incorporated rank–graduation accuracy for precision and rank–graduation explainability for component analysis. As a benchmark for comparison, the VARX–DHR and the Facebook Prophet models were used. Our results reveal that the VT–ARMA copula approach performed well in terms of accuracy, which was approximately 0.99 under the best specification. Furthermore, the copula component presented greater explainability than the autoregressive and moving–average components. In addition, residual diagnostics show significantly lower autocorrelation and partial autocorrelation with respect to the original data, and that the residuals are approximately normally distributed. Overall, the method developed in this study could provide valuable insights supporting urban planners and analysts in making informed decisions.

B) Short paper proceedings

1. Perazzini, S., Metulini, R. (2025). Exploring Urban Mobility Patterns in Lombardia Through Advanced Analysis of Mobile Phone Data. In: Pollice, A., Mariani, P. (eds) Methodological and Applied Statistics and Demography II. SIS 2024. Italian Statistical Society Series on Advances in Statistics. Springer, Cham. doi: 10.1007/978-3-031-64350-7 71

Abstract

Accurately predicting people’s movements within a small area is crucial for urban planning, transportation optimization, and emergency response preparedness. In this respect, emerging time series models tailored to handle complex seasonal patterns show promising potential. Identifying the most effective model for capturing traffic flows is of utmost importance for informed decision-making by policymakers. In this study, we compare the predictive performance of two approaches: a vector autoregressive model with dynamic harmonic components and the Facebook Prophet model. To this aim, we capture human mobility using data from the mobile phone network and analyze three traffic flow types (inflows, outflows, and internal flows) in Cellatica, a Municipality in the Province of Brescia. Employing a cross-validation strategy, we assess the models’ predictive ability using the MAPE. Our findings suggest that the multivariate model, which can capture the intricate correlation structure among various flow types, yields consistently better forecasts of traffic flows.

2. Carpita, M., Metulini, R., Migliorati, M. (2025). Characteristic-based clustering of traffic flow time series with complex seasonality. In: Book of papers IES 2025 - Innovation & Society: Statistics and Data Science for Evaluation and Quality, Eds. G. Boccuzzo, E. Bovo, M. Manisera, L. Salmaso, pp. 952-958.

Abstract

Accurate prediction of people’s mobility from/to different areas is essential for urban planning, transportation optimization, and emergency management. We achieved reasonable forecasting accuracy by applying a trivariate VARX+DHR model to one year of hourly mobile phone traffic data from a high-flood-risk area in Brescia. Still, residuals are not normally distributed, with heavy tails and time-varying heteroskedasticity. We applied an GARCH approach to decompose volatility into daily, hourly, and intradaily components to address this issue. In this work, these volatility series are employed in a characteristic-based time series clustering strategy, in which some statistical features along with selected GARCH parameters, are combined with a k-means and fuzzy clustering methods to identify similar mobility patterns across the areas studied.

3. Guerini, S.S., Metulini, R. (2025). Assessing Predictive Performance of Time Series Copula Models in Traffic Flow Analysis. In: Book of papers IES 2025 - Innovation & Society: Statistics and Data Science for Evaluation and Quality, Eds. G. Boccuzzo, E. Bovo, M. Manisera, L. Salmaso, pp. 936-943.

Abstract

This study leverages the Vine-Transform ARMA Copula to model traffic data, with particular emphasis on evaluating predictive performance. To do so, origin-destination real-life mobile phone data have been used. Performance evaluation was conducted using the rank-graduation box approach along with a moving window cross-validation strategy, incorporating rank-graduation accuracy for precision and rank-graduation explainability for component analysis. As a benchmark for comparison, the Prophet model by Facebook was used. Preliminary results reveal that the Vine-Transform ARMA Copula approach outperforms the Prophet model in terms of accuracy. Furthermore, we show that the copula component presents greater explainability compared to the autoregressive and moving average components. The enhanced explainability of the copula component could provide valuable insights into complex dependency patterns, supporting urban planners and analysts in making informed decisions.

4. Adam, R., Biancalani, F., Metulini, R. (2025). Traffic Restrictions and Air Quality: A Counterfactual Matrix Completion Analysis of Milan’s Area C. In: Book of papers IES 2025 - Innovation & Society: Statistics and Data Science for Evaluation and Quality, Eds. G. Boccuzzo, E. Bovo, M. Manisera, L. Salmaso, pp. 944-951.

Abstract

Urban traffic is seen as one of the major contributors to air pollution in densely populated areas. Many cities have implemented traffic restriction zones to mitigate the high levels of pollutants within urban areas. Milan’s Area C, introduced in January 2012, is a prominent case. While prior studies utilizing classical econometric techniques have produced mixed results, we apply matrix completion, a statistical learning method, to evaluate the causal effect of Area C on air quality. Our analysis reveals a statistically significant reduction in PM10 levels due to Area C restrictions within the treated area.

5. Carpita, M., Metulini, R., Migliorati, M. (2025). Volatility decomposition of traffic flow time series with complex seasonality using GARCH models. In: Book of short papers of the ASA Rome Conference 2024, Supplement to Volume 37/2 of Statistica Applicata - Italian Journal of Applied Statistics. Padua: Cleup. pp. 127-132. DOI: doi.org/10.26398/asaproc.091

6. Shaukat, M. H., Finazzi, F. (2025). Statistical analysis of smartphone mobility data for air quality assessment.  In: Book of short papers of the ASA Rome Conference 2024, Supplement to Volume 37/2 of Statistica Applicata - Italian Journal of Applied Statistics. Padua: Cleup. pp. 127-132. DOI: doi.org/10.26398/asaproc.0134

7. Guerini, S.S., Spezia, L. (2025). Copula functions and dynamic hydrological data: The case of Scotland. In: Book of short papers of the ASA Rome Conference 2024, Supplement to Volume 37/2 of Statistica Applicata - Italian Journal of Applied Statistics. Padua: Cleup. pp. 127-132. DOI: doi.org/10.26398/asaproc.0115

8.  Carpita, M., Metulini, R., Migliorati, M. (2026). Fuzzy clustering of GARCH components for traffic flow time series with complex seasonality. In: Statistical Methods for Data Analysis and Decision Sciences (Eds: F. De Battisti, S. Leorato, C. Masci, F. Nicolussi) ISBN: 978-3-032-18987-5