# Questions tagged [nonlinear-dynamical-system]

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### Representation of Hessian in Augmented State-Space Filtering Problems

Question Let $z_t := (x_t, x_{t-1}, x_t^2, x_{t-1}x_t,x_{t-1}x_t,x_{t-1}^2)$, and $R(x_t) := \sum_{(i,j) \in \{\{0,1,2,3,4\} \otimes \{0,1,2,3,4\} : i+j \le 4\}} w_{i,j} x_t^i x_{t-1}^j$, so $R(\cdot)$...
1 vote
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### Research field of timeseries with unpaired measurements?

I have measurements of cells' gene expression at different time points (t0, t1, t2, ...). Cells die when measured and therefore all measurements are from different samples, i.e. I do not observe any ...
• 219
1 vote
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1 vote
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### TVP-VAR fails statespace.MLEModel

I am trying to run a TVP-VAR for a panel in python using statsmodels. I am using the site example, trying to adopt it in my model. Data are from 1945-2020 for 50 countries Furthermore, I am getting ...
• 31
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### Meaning of a scaling constant in a well-calibrated model

I'm reading this paper on safe model-based reinforcement learning. Assumption 2 in this paper states: Let $\mu_n(\cdot)$ and $\Sigma_n(\cdot)$ denote the posterior mean and covariance matrix ...
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### Do stochastic chaotic systems decorrelate with time?

Assume I have a dynamical system with additive process noise of the form $$\mathbf{x}_{t} = \mathbf{F}\left(\mathbf{x_{t-1}}\right) + \mathbf{\epsilon}$$ where $\mathbf{x}_{t}$ is the state at time $t$...
• 565
885 views

### Time Varying Coefficients vs Rolling Estimation

What are the practical differences for forecasting from fitting a model with time varying coefficients vs. estimating a model with fixed parameters over rolling windows? Intuitively it seems that ...
• 600
1 vote
1k views

### Kalman Filter and Monte Carlo

What is the consequence on the uncertainty of our estimate when applying the standard kalman filter to nonlinear systems? If we are unaware of the functional form of these non linear systems how do ...
257 views

### Chaos theory, equation-free modeling and non-parametric statistics

Being interested in complex systems and trying to get a beginner's understanding of the field, today I ran across this interesting article in Quanta Magazine on chaos theory and equation-free modeling....
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