A nonhomogeneous hidden semi-Markov model is proposed to segment toroidal time series according to a finite number of latent regimes and, simultaneously, estimate the influence of time-varying covariates on the process' survival under each regime. The model is a mixture of toroidal densities, whose parameters depend on the evolution of a semi-Markov chain, which is in turn modulated by time-varying covariates through a proportional hazards assumption. Parameter estimates are obtained using an EM algorithm that relies on an efficient augmentation of the latent process. The proposal is illustrated on a time series of wind and wave directions recorded during winter.

翻译：本文提出一种非齐次隐半马尔可夫模型，用于根据有限个潜在状态分割环形时间序列，并同时估计时变协变量对各状态生存过程的影响。该模型是环形密度函数的混合模型，其参数依赖于半马尔可夫链的演变，而半马尔可夫链通过比例风险假设受时变协变量调制。采用基于潜在过程高效增广的EM算法进行参数估计。通过冬季记录的风向与波向时间序列实例验证了该方法的有效性。