Dear Colleagues,

On Thursday the 30th of May you are all warmly invited to our one-day workshop organised under the GRINS Project on *Time Series Models for Financial and Environmental Risk*

*https://www.unive.it/data/33113/3/88487 https://www.unive.it/data/agenda/3/88487*

Participation is free. However, for organizational purposes, you are kindly asked to register by May the 27th here

https://bit.ly/form-workshop-timeseriesmodels .

Ca’ Foscari University, San Giobbe Economics Campus, Meeting Room 1, Venezia

*Program:*

10.00am Registration

10.45am *Welcome Remarks: Prof. Monica Billio, Ca’ Foscari University of Venice, Project Leder of the Grins Spoke 4, Sustainable Finance.*

*1st Session*

11.00am *Prof.* *Giacomo Bormetti, University of Pavia*, *Measuring price impact and information content of trades in a time-varying setting.*

11.45am *Dr. Giuseppe Buccheri, University of Verona*, *Semiparametric Estimation of Volatility in the Presence of Intraday Drift Dynamics.*

12.30pm Lunch

*2nd Session*

2.00pm* Dr. Dario Palumbo, Ca' Foscari University of Venice*, *An Observation-Driven Generalized Poisson Model*.

2.45pm *Dr. Enzo D'Innocenzo, University of Bologna, **Limit results for score-driven filters**.*

3.30pm Coffee break

4.00pm *Keynote speech**: Prof. Andrew Harvey, University of Cambridge. **Score-driven models: overview and recent developments.*

*Abstracts*:

*Prof.* *Giacomo Bormetti,*University of Pavia, Italy https://unipv.unifind.cineca.it/get/person/021642 https://warwick.ac.uk/dfirth

*Measuring price impact and information content of trades in a time-varying setting*

We propose a non-linear observation-driven version of the Hasbrouck (1991) model for dynamically estimating trades' market impact and information content. We find that market impact displays an intraday pattern superimposed with large fluctuations. Some of them are exogenous, and, as an example, we investigate market impact dynamics around FOMC announcements. Contrary to Hasbrouck (1991), we find that the information content of trades depends on the local liquidity level and the recent history of prices and trades. Finally, we use the model to estimate the time-varying permanent impact parameter, which allows performing a dynamic transaction cost analysis.

Joint work with Francesco Campigli and Fabrizio Lillo.

*Dr. Giuseppe Buccheri,*University of Verona, Italy https://sites.google.com/view/giuseppe-buccheri/home https://www.ikosmidis.com/

*Semiparametric Estimation of Volatility in the Presence of Intraday Drift Dynamics*

In the conventional semimartingale representation of the log-price of a financial security, the volatility of daily log-returns is consistently estimated by their ex-post quadratic variation. A crucial assumption underlying this result is that the drift dynamics are negligible or pre-determined given past information. Recent empirical evidences of intraday unanticipated variations of mean returns call into doubt the validity of this assumption. We propose a semiparametric estimator of the daily return volatility incorporating the effect of stochastic intraday dynamics of the drift process. This framework allows us to test for the presence of drift dynamics in the data and to assess their impact on the daily return volatility. Our empirical analysis shows three main results: (i) there exists compelling evidence of intraday drift dynamics across various asset classes; (ii) when the drift moves significantly, our measure of volatility provides a better description of the return distribution; (iii) the component of the return variance associated with drift dynamics is non-negligible and possesses predictive power.

Joint work with Giorgio Vocalelli.

*Dr. Dario Palumbo,* Ca' Foscari University of Venice, Italy https://www.unive.it/data/people/22437798

*An Observation-Driven Generalized Poisson Model for Environmental Variables*

Based on the Generalised Poisson (GP) conditional distribution, a new general class of observation-driven models for count data is presented and their theoretical properties are derived. The GP is a flexible distribution which allows for both under- and over-dispersion. As a special member of this class, a score-driven model version is introduced. We show that this specification is robust to the presence of outliers and can be extended to allow for time varying over-dispersion. For the estimation of the model we provide a Bayesian inference framework and an efficient posterior approximation procedure based on Markov Chain Monte Carlo. The applications on environmental variables show that the proposed model is well suited for capturing the over-dispersion feature of the data.

*Dr. Enzo D'Innocenzo,* University of Bologna, Italy https://www.enzodinnocenzo.com/ https://researchportal.uc3m.es/display/inv16189

*Limit results for score-driven filters*

A study of the filtering approximation-theoretic properties of score-driven time series models. The new results are derived under a set of Lipschitz-type and tail conditions, from which I obtain maximal and deviation inequalities for the filtering approximation error. For the latter, I use techniques from empirical process theory. The novel proposed approach allows, for the first time, to study the asymptotic behavior of the empirical distribution function and the empirical processes of the approximated residuals. Since score-driven models encompasses the well-known generalized autoregressive conditional heteroskedasticity, it is proved that the results obtained in this paper extends those of Francq and Zakoian (2022) for this class of nonlinear models. In conclusion, I also give an application of these results to a popular score-driven time series models, namely, the Beta-t-GARCH(1,1) model.

*Prof. Andrew Harvey,*University of Cambridge, UK *https://www.econ.cam.ac.uk/people/emeritus/ach34 https://www.econ.cam.ac.uk/people/emeritus/ach34*

*Score-driven models: overview and recent developments*

Score-driven <ach34@cam.ac.uk)Score-driven> time series models were introduced into the literature more than a decade ago. Since then progress has been made on the theory and a variety of new models have been introduced. I begin by reviewing theoretical results on stationarity and invertibility and show how these apply to moment-driven and score-driven models for dynamic location and/or scale parameters from a wide range of distributions. Issues of robustness are discussed and it is argued that quasi score-driven (QSD) models have an important role to play. The advantages of an exponential link function are stressed. In particular it is argued that (Q)SD-EGARCH models are much better than standard (moment-driven) GARCH models. I finish by showing how the score-driven approach solves two difficult problems: constructing time series models for censored observations and circular data.