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Samuel Modée

Publications and source records attributed to Samuel Modée.

2 recordsLinked to original sources

Multi-regime Markov-switching models with time-varying transition probabilities: An application to U.S. Treasury yields

This paper studies Markov-switching (MS) models with time-varying transition probabilities (TVTP) under alternative specifications of the transition probability matrix. We extend the two-regime common-variance setting of the Generalized Autoregressive Score (GAS) model of Bazzi et al. (2017) to the general $K$-regime case with regime-specific means and variances, and develop an open-source R package, multiregimeTVTP, for simulation and estimation of such models. A Monte Carlo study shows that the regime means, variances, and transition probabilities are reliably recovered, whereas the TVTP driving coefficients are harder to identify. The GAS score coefficient appears to be statistically non-identifiable, owing to a ridge in the likelihood surface linking it to the regime variance. The filtered regime probabilities are accurately recovered under correct specification, whereas the one-step-ahead conditional mean is insensitive to misspecification of the transition dynamics. An empirical application to U.S. Treasury zero-coupon yield changes (1961-2024) at four maturities shows that a specification driven by the lagged yield level provides the best fit, attaining the lowest AIC at all four maturities and the lowest BIC at the short end of the yield curve, and that the estimated regimes align with documented episodes of U.S. monetary history.

stat.ME

The Zombie Infection Model

We study a variant of the stochastic SIR model on graphs that has previously been introduced in the physics literature for modelling zombie outbreaks and here referred to as the Zombie Infection Model (ZIM). In this model, initially each node of a graph is either susceptible, infected or removed. As in the SIR model, a susceptible node becomes infected at rate $λ$ times the number of its infected neighbours. Moreover, in the ZIM, an infected node is removed at rate $1$ times the number of its susceptible neighbours. This process exhibits rich and sometimes counterintuitive behaviour. By combining various coupling techniques, we provide a rigorous mathematical analysis of the model, focusing on monotonicity properties and the probability of the infection spreading indefinitely. One of our main results is that this probability is monotone with respect to an increase of $λ$ for the process on trees, but that there are graphs of bounded degree for which it is continuous and yet not monotone. We also establish bounds on this probability for the process on general graphs, and derive more precise results for complete graphs, regular trees, and the $d$-dimensional integer lattice.

math.PR