# Econometrics and Statistics Seminar

**Time and place:** Thursdays, 14:00-15:00 h in the Faculty Lounge (Room 0.036), Juridicum, Adenauerallee 24-42, 53113 Bonn

**October 17, 2019 - Bettina Siﬂinger (Tilburg University)**

**November 14, 2019 - Sven Otto (University Bonn)"A Dynamic Functional Factor Model for Yield Curves: Identification, Estimation, and Prediction"Abstract:** The problem of yield curve forecasting from a functional time series perspective is discussed. A functional factor model is considered, in which the factors follow some linear autoregressive process. The model is identified by imposing suitable conditions on the factors and the loading functions. By applying the least squares principle, a functional principal components based estimator is obtained, which is shown to be consistent. The minimum mean squared error forecast from the dynamic functional factor model is considered, and pointwise and simultaneous prediction bands are derived. Finally, the accuracy of the predictions and prediction bands is discussed in an out-of-sample experiment with monthly yield curves of U.S. Treasuries.

**November 21, 2019 - Lionel Truquet (ENSAI)" Iterations of dependent random maps and exogeneity in nonlinear dynamics"Abstract:** Among the various contributions devoted to time series analysis, theoretical results justifying stationarity and ergodicity properties of some standard stochastic processes when exogenous covariates are incorporated in the dynamic are rather scarce. In this talk, we will present some results when the process can be defined from random maps satisfying Lipschitz type properties and when the exogeneity is not necessarily strict. We will first remind the notion of Lyapunov exponent and we will also present a new result of stability when the classical condition of "contraction on average" is replaced with a contraction in conditional expectation. Under some conditions, we also derive an explicit control of the functional dependence of Wu (2005) which guarantees a wide range of statistical applications. Our results are illustrated with CHARN models, GARCH processes, count time series, binary choice models and categorical time series for which we provide many extensions of existing results.

**December 19, 2019 - Paul Doukhan (University Cergy-Pontoise)"Non-stationarity and applications"**

**Abstract:**The notion of stationarity has more a mathematical origin than a tight relationship to real data sets. Namely the underlying idea of this assumption is the use of the ergodic theorem (the law of large numbers). The aim of the talk is to try to provide mathematical models adapted to several issues of real data. We aim also at precisely setting some technical ideas for fitting such models. We will describe some models for astronomical data sets, in order to exhibit precise features of interest for real models, and we will try to avoid the standard mathematical traps to pass from stationary models to non stationary ones. Namely local stationarity, periods, exogenous data and isotonic assumptions are clearly seen to be reasonable. Weak dependence conditions are also quite valuable in such settings.

**January 16, 2020 - Frédéric Ferraty (University Toulouse III)"Scalar-on-function local linear regression and beyond"Abstract:** Regressing a scalar response on a random function (i.e. random variable taking values in function space) is nowadays a common situation. In the nonparametric setting, this paper paves the way for making the local linear regression based on a projection approach a prominent method for solving this regression problem. Our asymptotic results demonstrate that the functional local linear regression outperforms its functional local constant counterpart. Beyond the estimation of the regression operator itself, the local linear regression is also a useful tool for predicting the functional derivative of the regression operator, a promising mathematical object on its own. The local linear estimator of the functional derivative is shown to be consistent. On simulated datasets we illustrate good finite sample properties of both proposed methods. On a real data example of a single-functional index model we indicate how the functional derivative of the regression operator provides an original and fast, widely applicable estimating method. This methodology is extended to the multiple-functional index model with a surprising 2-step estimating procedure.

**January 23, 2020, 14-15 Uhr - Göran Kauermann (LMU Munich)****"Temporal Network Models - or - Understanding the Trading of Arms"Abstract:** The talk starts with an introduction to Exponential Random Graph Models (ERGM), the statistical work-horse model for the analysis of network data. We demonstrate the central modeling idea and discuss estimation strategies. The model class of ERGMs is then extended towards dynamic models, that is for network data which are observed at different time-points t=1,….T. We discuss two central models in this field. First, the temporal Exponential Random Graph Model (tERGM), which is an extension of the classical ERGM by allowing network statistics to depend on previous networks. Secondly, we introduce the separable temporal Exponential Random Graph Model (stERGM), which allows to decompose temporal changes into edges that develop and edges that vanish from one time-point to the next. The models are applied to network data on arm trading, provided by the Stockholm Peace Research Institute (SIPRI). The data give inter-state arm trading of heavy conventional weapons (tanks, air crafts, missiles etc.) from the 50th up to the recent years. We explore what drives the changes in the network by employing the two proposed temporal network models.