Questions tagged [state-space-models]
It describes the probabilistic dependence between the latent state variable and the observed measurement.
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9 views
Error: in ‘simulate’: argument “params” is missing, with no default [migrated]
Hey I am learning package 'pomp' recently. And I don't know why there is such an error in my code, the source is from paper https://kingaa.github.io/pomp/vignettes/pompjss.pdf
...
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0answers
12 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
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1answer
82 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
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1answer
33 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 ...
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0answers
58 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
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1answer
21 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 ...
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0answers
21 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 ...
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0answers
21 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 ...
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17 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....
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3answers
85 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:
$$\xi_{t+1} = F\xi_t + v_{t+1}$$
$$y_t = H\xi_t + w_{t}$$
...
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0answers
9 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 ...
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0answers
58 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 ...
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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
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0answers
21 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 ...
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0answers
64 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}...
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0answers
10 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 ...
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0answers
50 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
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1answer
45 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
32 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
21 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 ...
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42 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 ...
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0answers
32 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
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1answer
74 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 ...
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0answers
64 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
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1answer
30 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 ...
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1answer
30 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
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0answers
67 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-...
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0answers
42 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
25 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 ...
0
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0answers
14 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
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0answers
41 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
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1answer
59 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
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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 ...
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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
56 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)$$
where $...
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1answer
69 views
(Online) intuitive explanation of state space models
I have a similar question to the one in the link below:
Intuitive explanation of state space models
In the link they recommend the book by Commandeur and Koopman. I have this book already.
I was ...
0
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1answer
470 views
Examples of state space models where the filtering problem can be solved analytically
Background
A discrete-time, Markovian state space model takes the form
\begin{align}
\mathbf{y}_t&\sim p(\mathbf{y}_t\,|\,\mathbf{s}_t,\,\boldsymbol{\theta})\\
\mathbf{s}_t&\sim p(\mathbf{s}...
2
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0answers
82 views
Infill likelihood for a continuously observed continuous-time process
Consider a continuous-time stochastic process $y(t)$ having the following linear
(Gaussian) state-space representation for $t \geq 0$
$$
\left\{
\begin{array}{c c l}
\text{d}{\boldsymbol{\...
2
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0answers
24 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 ...
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0answers
101 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
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0answers
101 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 ...
1
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1answer
77 views
State-space model with contemporaneous effects
I have the following system of equations:
$$
\begin{align}
y_t^{(1)}&=y_t^{(2)}-x_t+\epsilon_t\\
y_t^{(2)}&=x_t+\nu_t\\
x_t&=\alpha x_{t-1}+u_t
\end{align}
$$
where $y_t^{(1)}, y_t^{(2)}$ ...
1
vote
2answers
113 views
Kalman Filter Derivation - Shumway / Stoffer
I'm going through the proof of the Kalman filter equations in Shumway, Stoffer - Time Series Analysis and its applications. Could someone please tell me how equation (6.26) is justified? How can we ...
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1answer
227 views
Estimating State Space Model Parameters
I'm having a bit of difficulty estimating parameters in DLM in R and I was wondering if I could get a bit of help with it. I have a system of equations given as:
$p_{t} = m_{t} + s_{t}$
$m_{t} = m_{...
3
votes
1answer
104 views
State Space Model Form for Equations
I have a set of equations which I have to write in state space model form but unfortunately I'm having a bit of difficulty doing so. They are given as:
$y_{t} = x_{t} + z_{t}$
$x_{t} = x_{t-1} + w_{...
2
votes
1answer
134 views
Deriving a filter like a Kalman filter from a non-Gaussian state space model
Assume we specify a state space model as
$$Y_t = a X_t + W_t$$
and
$$X_{t+1} = b X_t + V_t$$
where $b,a \in R$, $E[W_t] = E[V_t] = 0 \quad \forall{t }$ and $W_t $ and $V_t$ are indipendent for ...
1
vote
3answers
1k views
Simple explanation of dynamic linear models
I'm looking for a really simple explanation of what a dynamic linear model is as I need to explain this to a non-technical audience. I have looked around for examples but they are very maths heavy.
I ...
1
vote
1answer
43 views
Why is Qk not included in the cost function that is optimised by the Kalman filter?
Assume the following linear discrete system:
$x_k = Fx_{k-1} + w_{k-1}$ where $w_{k} \sim N(0, Q)$
$y_k = Hx_k + v_{k}$ where $v_{k} \sim N(0, R)$
One way to prove that the Kalman filter is optimal ...
-1
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2answers
44 views
Variance of a mixture of Normals with same $\sigma^2_i$
Let $Y\sim \sum^N_{i=1}\omega_iN(m_i,h^2 V)$.
The text I'm reading states that $Var(Y)=(1+h^2)V$, when $m_i=\theta_i$, where $\theta_i$ are draws taken from $P(\theta|D)$, and $V=Var(\theta|D)$
I ...
0
votes
1answer
132 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 \...
