Maximum likelihood inference for a class of discrete-time Markov switching time series models with multiple delays

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...

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Bibliographic Details
Published in:EURASIP journal on advances in signal processing 2024-07, Vol.2024 (1), p.74-29, Article 74
Main Authors: Martínez-Ordoñez, José. A., López-Santiago, Javier, Miguez, Joaquín
Format: Article
Language:English
Subjects:
Analysis
Delay difference equations
Differential equations
Discretization
Dynamic models
El Nino
Engineering
ENSO
Estimation
Expectation maximisation algorithm
Inference
Integers
Markov switch
Maximum likelihood estimation
Parameters
Quantum Information Technology
Signal,Image and Speech Processing
Southern Oscillation
Spintronics
Switching
Time series
Time series models
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Summary: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.
ISSN:1687-6180
1687-6172
1687-6180
DOI:10.1186/s13634-024-01166-8