Skip to main content

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.

Filter by
Sorted by
Tagged with
0 votes
1 answer
23 views

Computing prediction interval on discrete dynamical system forecast

Apologies if this is a basic question. Let's say I have a dynamical process $x_{n+1}=Ax_n+\varepsilon_n,$ where $A$ is an $m\times m$ matrix and $\varepsilon_n=(\varepsilon_{1,n},\varepsilon_{2,n},\...
Matt Helton's user avatar
0 votes
0 answers
110 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 ...
HelenA's user avatar
  • 11
1 vote
0 answers
201 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 ...
David K's user avatar
  • 31
1 vote
0 answers
76 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 ...
MikeRand's user avatar
  • 432
2 votes
0 answers
113 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 ...
Archie42's user avatar
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 $t$...
J.Galt's user avatar
  • 565
1 vote
1 answer
668 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)...
Thijs de Jongh's user avatar
1 vote
1 answer
135 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 ...
manav's user avatar
  • 329
1 vote
0 answers
51 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} = (...
wundi777's user avatar
2 votes
1 answer
156 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 ...
jbuddy_13's user avatar
  • 3,334
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 ...
manav's user avatar
  • 329
1 vote
0 answers
19 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^...
lbf_1994's user avatar
  • 528
0 votes
1 answer
196 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 ...
Teo Protoulis's user avatar
1 vote
1 answer
51 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 ...
KRL's user avatar
  • 286
4 votes
2 answers
168 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 ...
An old man in the sea.'s user avatar
1 vote
0 answers
125 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 ${\...
user avatar
2 votes
1 answer
849 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, ...
Chris Moore's user avatar
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 ...
Jack2018's user avatar
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 \...
Drumy's user avatar
  • 160
1 vote
0 answers
249 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 ...
Vykta Wakandigara's user avatar
2 votes
0 answers
551 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, \...
user150395's user avatar
4 votes
1 answer
63 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 ...
theideasmith's user avatar
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 ...
Kashif's user avatar
  • 517
1 vote
0 answers
68 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 ...
Thani Smille Sparklle Shinne's user avatar
3 votes
0 answers
270 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 ...
Ben's user avatar
  • 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,...
MikeHuber's user avatar
  • 1,239
0 votes
1 answer
667 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. \...
GKS's user avatar
  • 143
1 vote
1 answer
317 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 ...
SKM's user avatar
  • 787
1 vote
1 answer
125 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 ...
Sarunas's user avatar
  • 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-...
magnaJ's user avatar
  • 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 ...
Ursus Frost's user avatar
3 votes
1 answer
417 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 ...
Remi D's user avatar
  • 285
2 votes
0 answers
67 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 ...
triomphe's user avatar
  • 877
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 $...
bayerj's user avatar
  • 13.9k
2 votes
2 answers
316 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 ...
bayerj's user avatar
  • 13.9k
1 vote
1 answer
521 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 ...
bayerj's user avatar
  • 13.9k