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<p>Copula state space models (SSMs) provide a nonlinear and non-Gaussian framework and have been effectively applied, yet their observability properties remain unexplored. Instead, proposed estimation methods were directly applied to real-world data, without verifying whether they perform reliably. We introduce a novel definition of observability and a numerical approach for assessing observability of general copula SSMs. Given an observation trajectory, we aim to recover the augmented state, which includes both parameters and the state trajectory. Observability depends on the existence of an appropriate estimator for the augmented state. In nonlinear SSMs, observability is not a global property; such an estimator may not exist for all possible observation and state trajectories. Since it is not possible to check all realizations, we consider selected ones - the point masses of a discrete density approximation (quasi-random, deterministic, low-discrepancy sampling), representing the joint distribution of observation and state trajectory. The point masses are called design trajectories. For computation, the Bayesian MCMC framework <Emphasis FontCategory="NonProportional">Stan</Emphasis> is chosen. Successful convergence indicates that the augmented state is recoverable; if this is not the case for any design trajectory, the model is considered unobservable. Additionally, we propose quantifying the degree of observability. We show a high degree of observability for copula SSMs where a series of univariate states describes (i) a single and (ii) <i>d</i> univariate time series.</p>

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On the Observability of Copula State Space Models using a Bayesian Approach

  • 期刊论文

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  • 发表日期：

    2026年7月4日

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  • Ariane Hanebeck,
  • Claudia Czado

摘要

Copula state space models (SSMs) provide a nonlinear and non-Gaussian framework and have been effectively applied, yet their observability properties remain unexplored. Instead, proposed estimation methods were directly applied to real-world data, without verifying whether they perform reliably. We introduce a novel definition of observability and a numerical approach for assessing observability of general copula SSMs. Given an observation trajectory, we aim to recover the augmented state, which includes both parameters and the state trajectory. Observability depends on the existence of an appropriate estimator for the augmented state. In nonlinear SSMs, observability is not a global property; such an estimator may not exist for all possible observation and state trajectories. Since it is not possible to check all realizations, we consider selected ones - the point masses of a discrete density approximation (quasi-random, deterministic, low-discrepancy sampling), representing the joint distribution of observation and state trajectory. The point masses are called design trajectories. For computation, the Bayesian MCMC framework Stan is chosen. Successful convergence indicates that the augmented state is recoverable; if this is not the case for any design trajectory, the model is considered unobservable. Additionally, we propose quantifying the degree of observability. We show a high degree of observability for copula SSMs where a series of univariate states describes (i) a single and (ii) d univariate time series.