Questions tagged [state-space-models]

It describes the probabilistic dependence between the latent state variable and the observed measurement.

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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 = ...
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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 ...
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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 ...
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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 ...
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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 &...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 \...
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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 ...
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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 ${\...
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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 ...
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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 ...
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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 ...
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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....
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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: $$\xi_{t+1} = F\xi_t + v_{t+1}$$ $$y_t = H\xi_t + w_{t}$$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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}...
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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 ...
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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 (...
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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\...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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, $y_i$ ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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
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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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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 ...
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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 $...
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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 ...
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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}...
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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{\...
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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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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 ...
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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 ...