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15 novembre 2022

Advances in Time Series

Advances in Time Series

Conférence organisée par le LMM dans le cadre de l'ANR EFFI 2022-2025.

Programme :

  • 9h30-10h30 : Christian Francq (ENSAE et Université de Lille, France) 

Autoregressive conditional betas

This paper introduces an autoregressive conditional beta (ACB) model that allows regressions with dynamic betas (or slope coefficients) and residuals with GARCH conditional volatility. The model is built from the Gaussian score-driven approach, but it is semi-parametric in the sense that the distributions of the innovations are not specified. The time-varying betas are allowed to depend on past shocks and exogenous variables. We establish the existence of a stationary solution for the ACB model, the invertibility of the score-driven filter for the time-varying betas, and the asymptotic properties of one-step and multistep QMLEs for the new ACB model. The finite sample properties of these estimators are studied by means of an extensive Monte Carlo study. Finally, we also propose a strategy to test for the constancy of the conditional betas. In a financial application, we find evidence for time-varying conditional betas and highlight the empirical relevance of the ACB model in a portfolio and risk management empirical exercise.

  • 11h00-12h00 : Erik Kole (Erasmus University Rotterdam, Pays-Bas)

High-Dimensional Dynamic Factor Models with Markov Switching 

Factor models have become the standard methodology used for forecasting in macro and finance. In this paper, we show how standard dynamic factor models can be extended with Markov-switching. This general class of models can accommodate the breaks and instabilities that have been documented with regard to factor models applied to large panels of time-series. We analyze model properties such as conditional moments and stationarity, propose estimation based on conditional expectation maximization, and propose forecasting techniques. In our empirical application we show the out-of-sample benefits of dynamic factor models with Markov-switching.

  • 14h00-15h00 : Frédéric Proia (Université Angers, France)  

Nearly-unstable processes

It is well-known that the stability of an autoregressive process only depends on the localization of the eigenvalues of its companion matrix. In particular, the process is stable when the spectral radius is inside the unit circle whereas it is unstable when it is on the unit circle, the other configurations leading to explosive behaviors. In an autoregressive process with time-varying coefficients, we can make the coefficients vary in a triangular form (a new model corresponds to each new observation). When the coefficients remain in the stable area but converge to an unstable state, we say that the process is stable but nearly-unstable. Such a model enables to focus on the unit roots phenomena. In this talk, we will introduce such processes together with suitable hypotheses, and we will study the estimation behavior (in terms of consistency, asymptotic normality and moderate deviations).

  • 15h30-16h30 : Alexander Aue (University of California, États-Unis)

Detecting deviations from stationarity of functional time series

The advent of complex data has led to increased research in virtually all areas of statistics, including functional data analysis (FDA). Within the purview of FDA, the use of methods for serially correlated functions is often prudent. As for simpler univariate time series models, the theoretical foundations of methodology are often laid exploiting the notion of stationarity, while data analysis is often conducted on data violating this assumption. This talk looks into ways of discovering departures from stationarity in two ways. In the first part, structural breaks are considered, such that the sample is split into segments in a non-smooth fashion. The methodology to be presented does not rely on the usual dimension reduction techniques, which might be advantageous if the structural break is not sparse (that is, not concentrated within the primary modes of variation of the data). In the second part, local stationarity is introduced as a smooth deviation from stationarity. Here methods in the frequency domain are considered, based on the general result that (second-order) stationarity is equivalent to a functional version of the periodogram being uncorrelated at the Fourier frequencies. Both sets of methods are illustrated with annual Australian temperature profiles. The talk is based on joint work with Anne van Delft (Columbia), Greg Rice (Waterloo) and Ozan Sönmez (formerly Davis).

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