🤖 AI Summary
This work addresses the limitations of traditional Markov switching models, which rely on fixed parametric transition functions and thus struggle to capture nonlinearities and context dependence in latent state dynamics. The authors propose a semiparametric state-space model in which state transition probabilities are defined via sigmoid-transformed nonlinear functions learned in either a reproducing kernel Hilbert space or a spline space. A generalized expectation-maximization algorithm is developed to jointly estimate the transition function and observation parameters. By relaxing rigid parametric assumptions, the approach substantially enhances the ability to model complex temporal latent-state dynamics. Theoretical guarantees—including identifiability and consistency of the estimators—are established. Empirical results demonstrate that the model more accurately recovers nonlinear transition mechanisms on synthetic data and achieves superior state classification and earlier regime detection on financial time series.
📝 Abstract
We develop a semi-parametric state-space model for time-series data with latent regime transitions. Classical Markov-switching models use fixed parametric transition functions, such as logistic or probit links, which restrict flexibility when transitions depend on nonlinear and context-dependent effects. We replace this assumption with learned functions $f_0, f_1 \in \calH$, where $\calH$ is either a reproducing kernel Hilbert space or a spline approximation space, and define transition probabilities as $p_{jk,t} = \sigmoid(f(\bx_{t-1}))$.
The transition functions are estimated jointly with emission parameters using a generalized Expectation-Maximization algorithm. The E-step uses the standard forward-backward recursion, while the M-step reduces to a penalized regression problem with weights from smoothed occupation measures. We establish identifiability conditions and provide a consistency argument for the resulting estimators.
Experiments on synthetic data show improved recovery of nonlinear transition dynamics compared to parametric baselines. An empirical study on financial time series demonstrates improved regime classification and earlier detection of transition events.