Dear All,

We have the pleasure thanks to the support of the ESSEC IDS dpt, Institut des Actuaires, LabEx MME-DII, the group BFA (SFdS), to invite you to the seminar by:

The complexity of real-world phenomena calls in for non-linear modelling and the class of threshold models has been recognized to be a flexible tool to describe complex features that characterize economic and financial phenomena. Since their introduction in late 1970s by Howell Tong [1990], Threshold Autoregressive Moving-Average (TARMA) models have gained popularity in economics and finance, especially in their autoregressive specification, the so-called Threshold Autoregressive (TAR) model. Despite the fact that the TARMA model is much more general and parsimonious than the TAR model, its theoretical developments was stuck for many years, due to unsolved theoretical problems, mainly due to its non-Markovian nature. Chan and Goracci [2019] solved the long-standing open problem regarding the probabilistic structure and made the first major breakthrough in TARMA modelling, thereby opening the door for substantial theoretical inferential developments and practical applications. In this talk, I present two recent methodological developments that can reveal useful in practical applications, especially in financial econometrics. First, I focus on bootstrap based supremum Lagrange Multiplier testing for threshold effects in time series models. Both the classical recursive residual i.i.d. bootstrap and a wild bootstrap is considered and their validity under the null hypothesis is proved. The framework is new, and requires the proof of non-standard results for bootstrap analysis in time series models; this includes a uniform bootstrap law of large numbers and a bootstrap functional central limit theorem. The work fills the long standing gap regarding the validity of the bootstrap when testing for threshold-type nonlinearity (Hansen [1996]). The tests can be used to detect the presence of non-linearity in situations where the estimated parameters indicate non-stationarity, or in presence of heteroskedasticity, as often witnessed in the analysis of financial data. Second, I present a test for threshold regulation in presence of measurement error. Regulation plays a fundamental role in fields such as economics, finance, among others. Growth processes are generally regulation-free until they enter extreme phases. For instance, real exchange rates are assumed to be regulated through a threshold that triggers the mean reversion toward zero. However, existing tests fail to reject the null hypothesis of a random walk, resulting in the so called purchasing power parity (PPP) puzzle. It is well known that existing unit-root tests can be severely biased in presence of moving-average components. Moreover they have low discriminating power against nonlinear alternatives. By leveraging the probabilistic properties of TARMA models, we develop a novel supremum Lagrange multiplier test for threshold regulation. To the best of our knowledge, this is the first unit-root test that specifies a moving average component both in the null and in the nonlinear alternative hypotheses. The empirical evidence confirms that the proposed approach has correct size and enjoys much higher power in terms of detecting regulation in dynamics than that of existing tests. The application to real exchange rates shows that TARMA models could represent a modest step toward a positive resolution of the PPP puzzle.