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The main component of the NextGeneration EU (NGEU) program is the Recovery and Resilience Facility (RRF), spanning an implementation period between 2021 and 2026. The RRF also includes a monitoring system: every six months, each country is required to send an update on the progress of the plan against 14 common indicators, measured on specific quantitative scales. The aim of this paper is to present the first empirical evidence on this system, while, at the same time, emphasizing the potential of its integration with the sustainable development framework (SDGs). We propose to develop a first linkage between the 14 common indicators and the SDGs which allows us to produce a composite index (SDGs-RRF) for France, Germany, Italy, and Spain for the period 2014-2021. Over this time, widespread improvements in the composite index across the four countries led to a partial reduction of the divergence. The proposed approach represents a first step towards a wider use of the SDGs for the assessment of the RRF, in line with their use in the European Semester documents prepared by the European Commission., Comment: 30 pages, in Italian, 10 figures, 13 tables

We focus on the time-varying modeling of VaR at a given coverage $\tau$, assessing whether the quantiles of the distribution of the returns standardized by their conditional means and standard deviations exhibit predictable dynamics. Models are evaluated via simulation, determining the merits of the asymmetric Mean Absolute Deviation as a loss function to rank forecast performances. The empirical application on the Fama-French 25 value-weighted portfolios with a moving forecast window shows substantial improvements in forecasting conditional quantiles by keeping the predicted quantile unchanged unless the empirical frequency of violations falls outside a data-driven interval around $\tau$., Comment: 37 pages, 5 figures, 8 tables

Central Banks interventions are frequent in response to exogenous events with direct implications on financial market volatility. In this paper, we introduce the Asymmetric Jump Multiplicative Error Model (AJM), which accounts for a specific jump component of volatility within an intradaily framework. Taking the Federal Reserve (Fed) as a reference, we propose a new model-based classification of monetary announcements based on their impact on the jump component of volatility. Focusing on a short window following each Fed's communication, we isolate the impact of monetary announcements from any contamination carried by relevant events that may occur within the same announcement day., Comment: 22 pages, 5 tables, 6 figures

Several phenomena are available representing market activity: volumes, number of trades, durations between trades or quotes, volatility - however measured - all share the feature to be represented as positive valued time series. When modeled, persistence in their behavior and reaction to new information suggested to adopt an autoregressive-type framework. The Multiplicative Error Model (MEM) is borne of an extension of the popular GARCH approach for modeling and forecasting conditional volatility of asset returns. It is obtained by multiplicatively combining the conditional expectation of a process (deterministically dependent upon an information set at a previous time period) with a random disturbance representing unpredictable news: MEMs have proved to parsimoniously achieve their task of producing good performing forecasts. In this paper we discuss various aspects of model specification and inference both for the univariate and the multivariate case. The applications are illustrative examples of how the presence of a slow moving low-frequency component can improve the properties of the estimated models., Comment: 29 pages

The financial turmoil surrounding the Great Recession called for unprecedented intervention by Central Banks: unconventional policies affected various areas in the economy, including stock market volatility. In order to evaluate such effects, by including Markov Switching dynamics within a recent Multiplicative Error Model, we propose a model--based classification of the dates of a Central Bank's announcements to distinguish the cases where the announcement implies an increase or a decrease in volatility, or no effect. In detail, we propose two smoothed probability--based classification methods, obtained as a by--product of the model estimation, which provide very similar results to those coming from a classical k--means clustering procedure. The application on four Eurozone market volatility series shows a successful classification of 144 European Central Bank announcements., Comment: 23 pages, 2 figures

Although quantile regression to calculate risk measures has been widely established in the financial literature, when considering data observed at mixed--frequency, an extension is needed. In this paper, a model is suggested built on a mixed--frequency quantile regression to directly estimate the Value--at--Risk (VaR) and the Expected Shortfall (ES) measures. In particular, the low--frequency component incorporates information coming from variables observed at, typically, monthly or lower frequencies, while the high--frequency component can include a variety of daily variables, like market indices or realized volatility measures. The conditions for the weak stationarity of the daily return process are derived and the finite sample properties are investigated in an extensive Monte Carlo exercise. The validity of the proposed model is then explored through a real data application using two energy commodities, namely, Crude Oil and Gasoline futures. Results show that our model outperforms other competing specifications, on the basis of some popular VaR and ES backtesting test procedures.

Taking the European Central Bank unconventional policies as a reference, we suggest a class of Multiplicative Error Models (MEM) taylored to analyze the impact such policies have on stock market volatility. The new set of models, called MEM with Asymmetry and Policy effects (MAP), keeps the base volatility dynamics separate from a component reproducing policy effects, with an increase in volatility on announcement days and a decrease unfolding implementation effects. When applied to four Eurozone markets, a Model Confidence Set approach finds a significant improvement of the forecasting power of the proxy after the Expanded Asset Purchase Programme implementation; a multi--step ahead forecasting exercise estimates the duration of the effect, and, by shocking the policy variable, we are able to quantify the reduction in volatility which is more marked for debt--troubled countries., Comment: 26 pages, 6 figures

We suggest the Doubly Multiplicative Error class of models (DMEM) for modeling and forecasting realized volatility, which combines two components accommodating low-, respectively, high-frequency features in the data. We derive the theoretical properties of the Maximum Likelihood and Generalized Method of Moments estimators. Two such models are then proposed, the Component-MEM, which uses daily data for both components, and the MEM-MIDAS, which exploits the logic of MIxed-DAta Sampling (MIDAS). The empirical application involves the S&P 500, NASDAQ, FTSE 100 and Hang Seng indices: irrespective of the market, both DMEM's outperform the HAR and other relevant GARCH-type models.

We build the time series of optimal realized portfolio weights from high-frequency data and we suggest a novel Dynamic Conditional Weights (DCW) model for their dynamics. DCW is benchmarked against popular model-based and model-free specifications in terms of weights forecasts and portfolio allocations. Next to portfolio variance, certainty equivalent and turnover, we introduce the break-even transaction costs as an additional measure that identifies the range of transaction costs for which one allocation is preferred to another. By comparing minimum-variance portfolios built on the components of the Dow Jones 30 Index, the proposed DCW overall attains the best allocations with respect to the measures considered, for any degree of risk-aversion, transaction costs and exposure.

The Multiplicative Error Model (Engle (2002)) for nonnegative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with nonnegative support. A multivariate extension allows for the innovations to be contemporaneously correlated. We overcome the lack of sufficiently flexible probability density functions for such processes by suggesting a copula function approach to estimate the parameters of the scale factors and of the correlations of the innovation processes. We illustrate this vector MEM with an application to the interactions between realized volatility, volume and the number of trades. We show that significantly superior realized volatility forecasts are delivered in the presence of other trading activity indicators and contemporaneous correlations., Comment: Financial support from Italian MIUR (PRIN 2010-2011 MISURA) gratefully acknowledged