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- Title
Maximum likelihood inference for a class of discrete-time Markov switching time series models with multiple delays.
- Authors
Martínez-Ordoñez, José. A.; López-Santiago, Javier; Miguez, Joaquín
- Abstract
Autoregressive Markov switching (ARMS) time series models are used to represent real-world signals whose dynamics may change over time. They have found application in many areas of the natural and social sciences, as well as in engineering. In general, inference in this kind of systems involves two problems: (a) detecting the number of distinct dynamical models that the signal may adopt and (b) estimating any unknown parameters in these models. In this paper, we introduce a new class of nonlinear ARMS time series models with delays that includes, among others, many systems resulting from the discretisation of stochastic delay differential equations (DDEs). Remarkably, this class includes cases in which the discretisation time grid is not necessarily aligned with the delays of the DDE, resulting in discrete-time ARMS models with real (non-integer) delays. The incorporation of real, possibly long, delays is a key departure compared to typical ARMS models in the literature. We describe methods for the maximum likelihood detection of the number of dynamical modes and the estimation of unknown parameters (including the possibly non-integer delays) and illustrate their application with a nonlinear ARMS model of El Niño–southern oscillation (ENSO) phenomenon.
- Subjects
TIME series analysis; MAXIMUM likelihood detection; EL Nino; DELAY differential equations; STOCHASTIC differential equations; MAXIMUM likelihood statistics; NONLINEAR dynamical systems; STOCHASTIC systems; PARAMETER estimation
- Publication
EURASIP Journal on Advances in Signal Processing, 2024, Vol 2024, Issue 1, p1
- ISSN
1687-6172
- Publication type
Article
- DOI
10.1186/s13634-024-01166-8