Questions tagged [state-space-models]
It describes the probabilistic dependence between the latent state variable and the observed measurement.
256
questions
1
vote
0answers
30 views
Questions about the stability (and stationarity) of a system and state space representations
I'm pretty new to the topic and I'm trying to understand how to determine the stability of a process. I'm giving this discrete-time stochastic system:
$$
\cases{ s_t = 2s_{t-2} + 3w_{t-2} \\
y_t = ...
1
vote
0answers
32 views
Predictions after SMC
I have a statistical model given by
$$
y_t\sim p(y_t|x_t, \theta)\\
x_t\sim p(x_t|x_{t-1},\theta)\\
\theta\sim p(\theta)
$$
where $y$ is the only observed component. Using a sequential Monte Carlo ...
0
votes
0answers
24 views
Outliers Kalman Filtering
This might not be the right place to ask this questions, but I figured it's more of a machine learning question. I am also asking on the pyro forum for brevity.
I'm working with the simple extended ...
0
votes
0answers
8 views
What is behind “forecast” in Eviews?
I have been trying to use state space models in order to represent some gestural data. Until now I have been using Eviews to to do all the dynamic forecasting part, so I was curious what is behind ...
0
votes
0answers
11 views
Transition Matrix definition in State Space models using gestural data
I am trying to represent some gestural data (x,y,z from right hand & x,y,z from left hand) I am getting from sensors in a state space form, so as to predict the next x,y,z.
Since statistics &...
0
votes
1answer
36 views
What are the differences between Bayesian filters and adaptive filters?
I am learning about state estimation and I am having difficulty understanding the difference between Bayesian filters such as Kalman filter and particle filters compared to adaptive filters. According ...
0
votes
0answers
9 views
Online learning from a Bayesian Perspective in a State-Space Model
I'm trying to learn how to do online learning from a Bayesian Perspective. My main interest is to use it for a State-Space model. However, any explanation/reference in a different context, which may ...
0
votes
0answers
29 views
Dynamic factor model (DFM) with R, please help
I'm interested doing a dynamic factor model (DLM) similar to Doz, Giannone and Reichlin (2011) and Giannone, Reichlin and Small (2008). Moreover, I'm trying doing macroeconomic nowcasting model.
In ...
1
vote
1answer
11 views
how to model a state space with GARCH noise
I'm trying to model a state space model with GARCH noise and get stuck by the complexity of the equation.
so the first equation is a observation equation and second one is a state equation where both ...
3
votes
2answers
87 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 ...
0
votes
0answers
15 views
Log innovation vs squared
I see some state space models specify their innovation process as log innovations and some squaring the term. For example, the examples in the R package DLM favours the use of log innovations when ...
2
votes
1answer
100 views
Are Kalman Filter recursions valid when the state noise has a singular covariance matrix?
Consider a Linear Gaussian State-Space Model where the states are denoted by $X_t$ and observations are denoted by $Y_t$:
\begin{align}
X_t &= A X_{t-1} + \epsilon_t, &&\epsilon_t \sim \...
1
vote
1answer
47 views
How to include seasonal effects into the system matrices of a state space model
I am working on learning state space models and am leaning heavily on this very helpful documentation. However, I'm really confused about the best way to include both a seasonal effect and dynamic ...
1
vote
0answers
63 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 ${\...
1
vote
1answer
25 views
How to infer state space parameters from an LSTM model?
I'm attempting to create a state-space model by training my time series data with an LSTM. I'm hoping the LSTM will capture non-linear phenomenon as opposed to a linear state-space model. The only ...
0
votes
0answers
22 views
How is the confidence metric of a state space model at a given state related to consumer demand for clickstream data?
I've been tasked to take over a project at my company where consumer demand for a given product is taken from the confidence metric of a given state of a state space model.
The way it works is that ...
0
votes
0answers
27 views
Equivalency between ARMAX and state-space model
I am trying to understand the equivalency between ARMAX and the state-space model. I have read articles/websites with different conclusions on this topic. Some people claim ARMAX and state-space model ...
0
votes
0answers
31 views
Confidence intervals for state space models
i'm looking for on how to calculate the following ICs: smoothing, on-line filter and prediction on state space models.
I'm not able to find any formula about them or any matlab command/class.
Thanks....
1
vote
3answers
120 views
Kalman filter parameter estimation
From what I've known about Kalman filter, it requires all the parameters of the underlying state space model. Say the state space model is:
$$\xi_{t+1} = F\xi_t + v_{t+1}$$
$$y_t = H\xi_t + w_{t}$$
...
0
votes
0answers
11 views
Estimating a changing transit time between inputs and output
I work with a chemical process in which there is a time lag between the inputs (raw material quality and cooking parameters) and the output (final product quality). The problem is that the time lag ...
2
votes
0answers
75 views
Eigenvalue decomposition of a covariance matrix using a fast Cholesky decomposition
Let $\mathbf{C}$ be a $n \times n$ covariance matrix and assume that
the LDL' Cholesky decomposition can be obtained efficiently. Can we
take advantage of this to obtain a fast eigenvalue ...
0
votes
0answers
10 views
Updating State-Space Holt-Winters Model Latent Variables
I'm trying to update the level at time t of a state-space, additive damped Holt-Winters model with a given ...
2
votes
0answers
23 views
State space estimation with state dependent state variance
I am estimating a state space of the following form
$$Y_t= A X_t + \epsilon_t$$
$$X_{t+1} = B X_{t} + \sigma \sqrt{( a-X_t)(X_t-b)} \eta_t$$
Considering the variance of the state error is state ...
0
votes
0answers
71 views
DLM regression with parameter restriction
Good afternoon,
I am attempting to fit a state space regression model of the form:
$Y_{t} = \beta_{1}Y_{t-1} + (1-\beta_{1})[i^* + \beta_{2}X_{t}] + \epsilon_{1,t}$
$i^* = i^*_{t-1} + \epsilon_{2,t}...
0
votes
0answers
11 views
Learning a Hopfield network parametrizing a Hamiltonian vs RNN
I think of an RNN as parametrizing a vector field. Say we forget about the inputs, and instead just want to learn a non-linear state space model. To make it more concrete, perhaps we want to model a ...
1
vote
0answers
60 views
particle filter marginal likelihood
I want to calculate the marginal likelihood $p(y|\Theta)$ of the parameters of a Markov state space model with unknown parameters $\Theta$ that I am trying to estimate the marginal likelihood (...
1
vote
1answer
54 views
Parameter estimation in Dynamic Linear Models
I am currently developing a DLM of the following form
$$\underset{k \times 1} {y_t} = \underset{k \times n}A \underset{n \times 1}{\theta_t} + \epsilon_t$$
$$\theta_t = \mu + \underset{n \times n}B\...
2
votes
1answer
33 views
likelihood of latent state space model
Im trying to calculate the likelihood function of my latent state space model.
My model has Poisson observations
$p(y_t|\beta_t;x_t) \sim \mathcal{Poiss}(z)$.
where $z$ is the rate of the poisson ...
0
votes
1answer
23 views
How do Tile Coding offsets still cover full state space / affect edge cases?
Reading Sutton & Barto I’m having a hard time visualizing the implementation of the tile coding discretization of states.
Specifically, if tilings are offset, how does this effect edge cases? For ...
0
votes
0answers
48 views
Using dlmMLE to estimate state space parameters
I have been trying to use the dlmMLE function from the R package dlm to estimate parameters ...
1
vote
0answers
39 views
AIC for latent variable models
I'm trying to use BIC/AIC for model comparison and want to know what the number of parameters is.
The models I'm unsure about are linear Gaussian state space models with nonlinear observations. ...
1
vote
1answer
81 views
computing the distribution over the latent function values with the form of a GP predictive
If we have a latent state space $\mathbf{X}$ and the observations $\mathbf{Y}$ and the transition function between two states $\mathbf{x}_{t-1}$ and $\mathbf{x}_{t}$ is given by $\mathbf{f}$ which is ...
1
vote
0answers
79 views
Multilevel dynamic linear models in R
I am interested in fitting a multilevel bayesian structural time series with a hierarchical structure of the dynamic regression coefficients. The reason I want to do this is is that I have a number of ...
0
votes
1answer
33 views
Custom Space State model using DLM in R
DLM package in R can model linear space state models of the form:
I have a different category of equation which is also a linear polynomial equation of order 1 with constant coefficients. I would ...
0
votes
1answer
31 views
What's the proper name for these chain structured PGMs?
I'm trying to find previous work that has dealt with this type of PGMs, but don't know what to call them:
a) "recurrent HMM"? $y_i$ are scalars and $x_i$ are discrete
b) "triangle HMM"? again, $y_i$ ...
1
vote
0answers
93 views
Proving Matrix-Normal-Inverse-Wishart distribution is a conjugate prior for a Linear Model
How does one prove that the Matrix-Normal-Inverse-Wishart distribution is a conjugate prior for a Linear Model? This prior is a generalization of the Normal-Inverse-Wishart Distribution.
By Matrix-...
1
vote
0answers
45 views
Hierarchical time series using DLM
I am developing a forecasting solution using R's dlm package and it is proving to be very useful for most of our requirements.
However, I am also keen on sharing information among different time ...
2
votes
0answers
27 views
Decomposition of interest rate risk premia
I have a question on econometric modelling techniques for decomposition. I have three variables:
- V1 which is an indicator of an interest rate risk premia
- V2 which is an indicator of a credit risk ...
1
vote
1answer
27 views
In a LGSSM how do we know that the prediction distribution is Gaussian?
I am trying to follow lecture notes regarding the Kalman Filter from a course taught at Stanford. The lecture notes can be found here.
The linear Gaussian state space model (LGSSM) is introduced as
...
2
votes
0answers
44 views
Time varying representation of Okun's law
I've estimated a dynamic linear model to capture time varying parameters in an Okun's law type of model:
I set the starting values for the state vector all equal to zero and estimate the system ...
1
vote
1answer
66 views
State space with lasso
Is it possible to incorporate lasso variable selection in the high dimensional state space model. If yes, is there any code or package available in R
0
votes
0answers
19 views
What is the intuition between using shared covariance parameters or separate in state space models?
I apologise if my terms aren't very exact as I'm in a learning process here, but would appreciate if you could provide me some intuition of what are the pros and cons of two alternatives.
I've got an ...
0
votes
0answers
9 views
Model for hormone levels over tissue cells
I have a certain type of biological data and I am unsure about how to model it.
The data represent the amount of 3 hormones detected along 20 consecutive cells of a certain plant tissue. I think there ...
4
votes
1answer
58 views
Conditional mean and co-variance in $VAR(p)$ conditional on one lag only
Suppose I have a $p$'th order vector auto regression
$$\vec Z_t = F_1\vec Z_{t-1}+F_2\vec Z_{t-2} + \cdots +F_p \vec Z_{t - p}
+ \vec \epsilon_t,\qquad \vec\epsilon_t\sim N_q(\vec0,Q)$$
where $...
0
votes
1answer
78 views
(Online) intuitive explanation of state space models
I have a similar question to the one in the link below:
Intuitive explanation of state space models
In the link they recommend the book by Commandeur and Koopman. I have this book already.
I was ...
0
votes
1answer
664 views
Examples of state space models where the filtering problem can be solved analytically
Background
A discrete-time, Markovian state space model takes the form
\begin{align}
\mathbf{y}_t&\sim p(\mathbf{y}_t\,|\,\mathbf{s}_t,\,\boldsymbol{\theta})\\
\mathbf{s}_t&\sim p(\mathbf{s}...
2
votes
0answers
82 views
Infill likelihood for a continuously observed continuous-time process
Consider a continuous-time stochastic process $y(t)$ having the following linear
(Gaussian) state-space representation for $t \geq 0$
$$
\left\{
\begin{array}{c c l}
\text{d}{\boldsymbol{\...
2
votes
0answers
26 views
Are there any R code examples for estimating the state space vector in this case?
I couldn't make sure Whether the model I'm using is a local level model with multiplicative components (state vector $\times$ regressor vector) or a linear gaussian state-space model. And couldn't ...
1
vote
0answers
110 views
Unable to recover time varying AR1 parameter from State Space model
I am trying to do a Time varying parameters regression. The equation is as follows:
$y_t = a + b_t * x_{1t} + \epsilon_t$
Here a is fixed while $b_t$ is AR1.
My state space equations are :
There ...
0
votes
0answers
128 views
Linear regression of features inside a hidden Markov model?
I have an interesting little problem which I am trying to attack using HMMs.
First, as usual, I am trying to do time-series segmentation/classification using a HMM. But the input to my HMM has an ...
