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.
38
questions
0
votes
0
answers
46
views
What are the advantages of model drift vs concept drift in online learning?
Let's say I have a simple linear predictor model and I want to update my model to adapt to the changes that have happened in the environment.
I mainly have two tools to detect dynamic changes:
Model ...
- 115
0
votes
0
answers
31
views
Conditions for statespace statsmodel mlemodel
I'm trying to run a TVP VAR on Statsmodel for a Big Data, but there seems to be a problem when trying to validate the vector matrix and the vector shape. Especially when defining the start and update ...
- 11
0
votes
0
answers
48
views
Estimate an ARMA disturbance model from measurement output data
Assume that we have a first order dynamical system
$$G(s) = \frac{1}{0.2s + 2.1}$$
I run this with an input $u = 10sin(t)$ and with gaussian noise.
...
- 349
0
votes
0
answers
92
views
Parameters in mlemodel in statsmodel
I am trying to run a TVP-VAR on statsmodel for a big data, but seems to run in a problem when I am trying to validate the vector matrix and the vector shape. Particularly, in the start and the update ...
- 11
1
vote
0
answers
125
views
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 ...
- 21
1
vote
0
answers
59
views
Multivariate time-series with asyncronous data
I have quote observations for 9 FX rates, which I would like to analyze via multivariate dynamic linear model (e.g., Chapter 16 in West and Harrison Bayesian Forecasting and Dynamic Models (1997).
In ...
- 412
2
votes
0
answers
85
views
Likelihood-ratio gradient estimator in linear dynamical system in python (Jax)
TL;DR
I am trying to implement the likelihood-ratio gradient estimator in a linear dynamical system (LDS) with Gaussian transition noise and Gaussian observation noise
I am currently using python and ...
- 21
2
votes
0
answers
50
views
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 $t$...
- 545
1
vote
1
answer
538
views
Exogenous variable in the state equation in statespace MLEmodel in statsmodels [closed]
I'm trying to fit the following model:
$y_t = \left[\begin{matrix} (1-w) & 1 & w \end{matrix}\right] \left[\begin{matrix} d_t \\ \mu_t \\ m_t \end{matrix}\right] + \mathcal{N}(0,\sigma_\eta^2)...
1
vote
1
answer
110
views
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 ...
- 321
1
vote
0
answers
47
views
Approximate a time-discrete linear-dynamical-system using a neural network, when only partial measurements are available
I want to use a simple neural network to approximate a linear time-discrete state-space model, given by the equation:
$$\boldsymbol{x}_{k+1} = \mathbf{A} \: \boldsymbol{x}_k$$
with
$$\boldsymbol{x} = (...
- 11
2
votes
1
answer
131
views
Getting started with Bayesian Dynamic Networks?
Dagum developed DBNs to unify and extend traditional linear
state-space models such as Kalman filters, linear and normal
forecasting models such as ARMA and simple dependency models such as
hidden ...
- 2,377
4
votes
1
answer
1k
views
initial conditions for statespace mlemodel in statsmodel
I am a bit puzzled by very sensitive dependence on the initial conditions in the statespace mlemodels in statsmodel. Let me take a concrete example here. I am trying to fit this Dynamic Linear model ...
- 321
1
vote
0
answers
16
views
Estimation of Linear Dynamical System with diagonality constraints
I am trying to estimate the parameters of the following linear dynamical system
\begin{align}
X_t &= \phi X_{t-1}+\varepsilon_t, \quad \varepsilon_t\sim N(0, \Sigma_\varepsilon)\\
Y_t & = h^...
- 528
0
votes
1
answer
154
views
Model evaluation using Akaike's Information Criterion, Bayesian Information Criterion and Future Prediction Error Criterion
I have come up with 5 different models for a dynamical process which has 3 parameters. In order to decide which model is the best, I am using these criterions from information theory: Akaike's ...
- 103
1
vote
1
answer
47
views
Examples of Real Applications for Time-series with Continuous-valued Targets and Continuous-valued Observations
Suppose that we are interested in estimating continuous-valued targets $y_t$ from continuous-valued observations $x_t$ over discrete time steps $t = \{1,2,3,\dots,T\}$. Could you give me some ...
- 206
4
votes
2
answers
165
views
Forecasting in a state-space model from a Bayesian perspective
We have the following state-space model(or linear dynamical model):
\begin{align}
x_t&\sim N(Ax_{t-1},Q)\\
y_t&\sim N(Bx_{t},\Sigma)
\end{align}
I want to obtain a sample from $p(y_{T+1}\mid ...
- 5,400
1
vote
0
answers
103
views
Does the Markov property always hold for a state-space structure?
Markov Property: $p({\bf x}_t | {\bf x}_1, \ldots, {\bf x}_{t-1}) = p({\bf x}_t | {\bf x}_{t-1})$
Consider the following model for which the hidden states are ${\bf x}_t$ and the observations are ${\...
user235125
2
votes
1
answer
785
views
How to numerically solve a matrix differential equation in R? [closed]
I have interest in using the R language and environment to numerically solve a system of linear ordinary differential equations. The numerical solver, deSolve, ...
- 211
0
votes
0
answers
69
views
How important is research on model selection methods in Statistics?
My question is nothing technical. I just wanted your opinion on how important is the model selection problem in the field of Statistics considering the age of big data. Are the current methods such as ...
- 31
0
votes
1
answer
1k
views
Convert a state-space model with exogenous input to one without
I have a state space model of the form
\begin{align}
x_{t+1} &= Ax_t + Bu_t + w_t\\
y_t &= Cx_t + Du_t + v_t
\end{align}
where $u$ is the exogenous input. Also, $ w_t \sim N(0, Q)$ and $v_t \...
- 160
1
vote
0
answers
229
views
How does one approximate $\mu$ and $\sigma$ in an arithmetic Brownian motion using a Kalman filter?
My concern arises from the fact that in the following system:
$x_k = (\mu, \sigma)^T = x_{k-1}$
$Y_k = Y_{k-1} + \mu + \sigma Z_k \quad Z_k \sim N(0,1)$
that I cannot separate the states I want to ...
2
votes
0
answers
532
views
How to ensure covariance matrix is positive semi definite in linear dynamical model learning?
I am trying to learn a linear dynamical model for a data using expectation-maximization algorithm. The model is defined as follows:
$$x_0 \sim \mathcal{N}(\mu_0 ,\Sigma_0)$$
$$ x_{t+1} = Fx_t + w_t, \...
- 21
4
votes
1
answer
61
views
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 ...
- 151
1
vote
0
answers
49
views
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 ...
- 507
1
vote
0
answers
67
views
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 ...
3
votes
0
answers
267
views
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 ...
- 207
1
vote
0
answers
37
views
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,...
- 1,229
0
votes
1
answer
641
views
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.
\...
- 143
1
vote
1
answer
297
views
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 ...
- 787
1
vote
1
answer
120
views
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 ...
- 410
2
votes
0
answers
160
views
State Space model question [closed]
I am looking for some help with estimating Space state model of this form:
$r_{t} = r^{*}_{t} + \pi + \varepsilon_{1}$
$R_{t}= r^{*}_{t} + \alpha + \pi + \varepsilon_{2}$
$r^{*}_{t} = r^{*}_{t-...
- 141
7
votes
2
answers
3k
views
Forward Filtering Backwards Sampling (FFBS) and Look-Ahead Bias
Assumptions / Context: Let's assume that I have data that can be modeled as a dynamic linear model. To estimate the parameters (e.g., covariance matrix of the state/system equation), I use a Gibbs ...
- 310
3
votes
1
answer
414
views
Model selection and parameter estimation in forecasting with a Dynamic Linear Model
I am implementing a general purpose prediction tool for time series. I want to tolerate missing values, so I decided to settle for DLMs. To make it as relevant as possible on a large number of ...
- 275
2
votes
0
answers
66
views
Estimation from two observations [closed]
Suppose there are two vector signals $x$, $z$. The observer 1 receives a linear version of $x$ plus Gaussian noise. Observer 2 receives a linear sum of both $x$ and $z$ plus Gaussian noise as shown ...
- 847
3
votes
0
answers
71
views
How to include prior knowledge that a model might be able to figure out itself
I have a problem where I want to predict the outcome of a sequence given another sequence online. Let $(x_1, x_2, ... x_T)$ be denoted by $x_{1:T}$, then I am estimating:
$$
p(y_T|x_{1:T})
$$
where $...
- 13.6k
2
votes
2
answers
311
views
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 ...
- 13.6k
1
vote
1
answer
508
views
Assumption of Gaussian distribution of acceleration
I have a data set consisting of noisy position values of a trajectory of a human hand. I want to estimate a generative model of these trajectories, and the obvious choice is a Kalman Filter/linear ...
- 13.6k