# Questions tagged [linear-dynamical-system]

Dynamic linear models refers to modeling problems where coefficients (as in regression) are allowed to vary with time. This is the so called state-space approach.

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### Choleskly constraint in mlemodel in statsmodel

I want to constraint the off diagonal terms in the covariance matrix in a dynamic linear model. I tried using Cholesky method but it does not seem to converge. I am trying to fit a multivariate CAPM ...
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### Help on statistical modeling of pedestrian flow in subways

I'm a New Yorker and take the subways every day. I have a growing interest in understanding the distribution of paths people take on the subways to work every day. I.e. if there are $n$ subway ...
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### Determining state space for a dynamic linear model

Are there any techniques for determining a good state space to use for a dynamic linear model? I'm trying to model ad-clicks with observed values being whether a user clicked on an ad and I'm curious ...
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### What should be the termination criteria for my problem with a closed loop system identification?

I have modelled a dynamic system which needs to be validated against test data. A closed loop system identification process is used for the validation. In this process, the time domain simulation of ...
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### How to add stochastic drift in dynamic linear model?

As I'm not able to comment (yet), my question follows the one raised by @mzuba here I would like to use the DLM R package to model the local linear trend model, which unlike mzuba specified, has a ...
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### Predictions in a control loop like airconditions

I wonder if there are special things to consider with predictions in a control loop, e.g. An airconditioner trys to hold the target temperature at 20 degrees. I want to predict the energy consumption,...
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### How to estimate coefficients of a state space when relevant data is provided?

I have a state space system $\dot{x}$ = $Ax$ + $Bu$ $y$ = $Cx$ I know C matrix exactly. And A matrix looks something like this, and some of the $x_{ij}$ in A are known as well. Same goes with B. \...
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### Help in CRLB for linear model

The model is an FIR (MA) filter $$x(t) = h_1 u(t-1) + h_2 u(t-2) + u(t) \tag{1}$$ $$y(t) = h^T x(t) + v(t) \tag{2}$$ $u(t)$ is a pseudo-random binary signal (PRBS) that excites/ drives the ...
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### Simulating a dynamical system

Basically I need to replicate Hartley's 'A User's Guide to Solving Real Business Cycle Models' . Specifically (to make question relevant to stats.stackexchange), I want to simulate the dynamical ...
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### Learning a mapping from one time series to another with a Kalman Filter

I am interested in finding the relation between two (possibly multi dimensional) time series $x_{1:T}$ and $y_{1:T}$. I wonder how I can do that with a linear dynamical system/Kalman filter. My ...
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