Job Market Paper

An Order-Invariant Score-Driven Dynamic Factor Model [Download] [WP version] [Best Graduate Paper in Macro Award at the IAAE 2023]
[submitted]

Abstract: This paper introduces a novel score-driven dynamic factor model designed for filtering cross-sectional co-movements in panels of time series. The model is formulated using elliptical distribution for the noise terms, thus allowing the update of the time-varying parameter to be potentially nonlinear and robust to outliers. We derive stochastic properties of the time series generated by the model, such as stationarity and ergodicity, and establish the invertibility of the filter. We prove that the identification of the factors and loadings is achieved by incorporating an orthogonality constraint on the loadings which is invariant to the order of the series in the panel. Given the nonlinearity of the constraint, we propose to exploit a maximum likelihood estimation on the Stiefel manifolds, which ensure that the identification constraint is satisfied numerically, hence allowing a joint estimation of the static and time-varying parameters. Furthermore, the asymptotic properties of the constrained estimator are derived. In a series of Monte Carlo experiments, we find evidence of appropriate finite sample properties of the estimator and resulting score filter for the time-varying parameters. We reveal the empirical usefulness of our factor model for constructing indices of economic activity from a set of macroeconomic and financial variables during the period 1981-2022. An empirical application highlights the importance of the robust update for the time-varying parameters in the presence of V-shaped recessions, such as the COVID-19 recession.

Publications

Score-Driven Models: Methodology and Theory, Oxford Research Encyclopedia of Economics and Finance, 2022. [Download, WP version]
(with Francisco Blasques, Janneke van Brummelen and Siem Jan Koopman)

Abstract: Score-driven models belong to a wider class of observation-driven time series models that are used intensively in empirical studies in economics and finance. A defining feature of the score-driven model is its mechanism of updating time-varying parameters by means of the score function of the predictive likelihood function. The class of score-driven models contains many other well-known observation-driven models as special cases, and many new models have been developed based on the score-driven principle. Score-driven models provide a general way of parameter updating, or filtering, in which all relevant features of the observation density function are considered. In models with fat-tailed observation densities, the score-driven updates are robust to large observations in time series. This kind of robustness is a convenient feature of score-driven models and makes them suitable for applications in finance and economics, where noisy data sets are regularly encountered. Parameter estimation for score-driven models is straightforward when the method of maximum likelihood is used. In many cases, theoretical results are available under rather general conditions.

Score-Driven Models: Methods and Applications, Oxford Research Encyclopedia of Economics and Finance, 2022. [Download, WP version]
(with Francisco Blasques, Janneke van Brummelen and Siem Jan Koopman)

Abstract: The flexibility, generality, and feasibility of score-driven models have contributed much to the impact of score-driven models in both research and policy. Score-driven models provide a unified framework for modeling the time-varying features in parametric models for time series. The predictive likelihood function is used as the driving mechanism for updating the time-varying parameters. It leads to a flexible, general, and intuitive way of modeling the dynamic features in the time series while the estimation and inference remain relatively simple. These properties remain valid when models rely on non-Gaussian densities and nonlinear dynamic structures. The class of score-driven models has become even more appealing since the developments in theory and methodology have progressed rapidly. Furthermore, new formulations of empirical dynamic models in this class have shown their relevance in economics and finance. In the context of macroeconomic studies, the key examples are nonlinear autoregressive, dynamic factor, dynamic spatial, and Markov-switching models. In the context of finance studies, the major examples are models for integer-valued time series, multivariate scale, and dynamic copula models. In finance applications, score-driven models are especially important because they provide particular updating mechanisms for time-varying parameters that limit the effect of the influential observations and outliers that are often present in financial time series.