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Questions tagged [state-space-models]

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

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1answer
23 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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0answers
13 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
7 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 ...
2
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0answers
34 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
36 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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0answers
51 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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65 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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0answers
14 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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63 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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0answers
15 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
66 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 $y_t^{(1)}, y_t^{(2)}$ ...
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2answers
91 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 ...
1
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1answer
144 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_{...
2
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1answer
81 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
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1answer
106 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 ...
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0answers
60 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 ...
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0answers
31 views

State space models with non stationary/unit root factors

state space model , I am trying to implement is as follows $$ Y_t= CY + FF* X_t + Ve_t$$ $$(X_t-m0)= GG (X_{t-1}-m0) +W\eta_t$$ I am enforcing GG to be to be diagonal for the base case. I am getting ...
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1answer
31 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 ...
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2answers
37 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 ...
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1answer
71 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 \...
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0answers
33 views

state space implementation using DLM FKF

state space model , I am trying to implement is as follows $$ y_t= CY + FF* X_t + Ve_t$$ $$(X_t-m0)= GG (X_{t-1}-m0) +W\eta_t$$ In DLM I am using following modification(because DLM does not allow ...
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0answers
59 views

How to approach SSM models for time series forecasting in general?

I have worked on SSM model using KFAS package (https://cran.r-project.org/web/packages/KFAS/KFAS.pdf) in R. Package suggests me to use one of the Box_Jenkins method to implement SSM. So we convert ...
4
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1answer
91 views

Coding resources: Accessible introductions to Bayesian Structural Time series?

Hello, all. I am asking this question in not necessarily a "subjectively recommend something for me" approach, but with a clear focus on just an accessible beginner's reference. My situation is I have ...
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0answers
44 views

R dynr: Having trouble setting up state-space model [closed]

I was looking around to flexibly implement state space models in R. I found dynr, but I am being frustrated to no end by its tad vague documentation and lack of ...
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2answers
132 views

A doubt on the notation of Frigola et al (2013) of Gaussian Processes(GP) for a State-Space model?

The picture above is from Frigola et al (2013) - Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC. In this paper, the authors later define $\mathbf{f}_t=f(\...
3
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1answer
79 views

Would a simple Gibbs, or a Metropolis-Hastings algorithm work for a State-Space model?

I'm wondering if a MCMC algorithm, in a Gibbs or a Metropolis-Hastings style, work for a State-Space model. Would I also be able to learn about the state variable and not just the parameters? I've ...
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0answers
137 views

ARIMA model for GDP

I am working through example 3.2.6 in 'Dynamic linear models with R' by Petris. I have download the quarterly deseasonalised USA GDP data located here: http://definetti.uark.edu/dlm/ (it's the data ...
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0answers
27 views

Assessing the fit of a state-space model in JAGS

I've been fitting a relatively complicated state-space model in JAGS and I want to do some basic model comparisons, including dropping parameters one at a time to assess their influence on the fit. ...
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0answers
151 views

traditional state-space models and LSTMs

I am trying to understand the nature of LSTMs in relation to intuitions from traditional state-space models (e.g., Kalman filtering). The code below aims to simulate a simple univariate linear state-...
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1answer
23 views

Introducing behavioural states into hidden markov model?

I have a hidden markov model which models movement. A map is split into even sized grids and the hidden states are the grids. I want to improve this model by adding behavioural states (so that ...
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0answers
82 views

Implementation of kalman filter with inner ARIMA non seasonal model

I am trying to write an application which impute some missing values on one time series signal. I have done it similarly in R using ImputeTS package but now need to do it similarly in Java. I just ...
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0answers
22 views

Splitting residuals in maximum likelihood estimation

I would like to estimate the parameters of a state space model with maximum likelihood. The model has non-smooth transition—I would like to split the estimated residuals into two groups dependent on ...
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0answers
46 views

How to predict changes in a signal based on other leading signals?

Goal: classify changes in green series using black series as predictor more specifically, create classification for when black series increased/decreased and n-seconds after black series moves then ...
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0answers
42 views

unscented kalman filter for non-linear state-space

I intend to use unscented kalman filter to estimate a non-linear state -space problem. latent factor $X_t$ in the formulation has usual VAR(1) specification $$X_t = \phi X_{t-1} +\epsilon_t$$ ...
2
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1answer
191 views

DLM representation of ARIMA models

I am working through example 3.2.6 in 'Dynamic linear models with R' by Petris. I have download the USA GDP data located here: http://definetti.uark.edu/dlm/ The example starts by estimating the ...
0
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1answer
31 views

State space model with third or more order trend

In state space model, a system model with first order trend is represented as $$ x_{t} = x_{t-1} + e_{t}, $$ where $x_{t}$ is system model, $e_{t}$ is system noise. Also, a system model with ...
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0answers
52 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 ...
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1answer
69 views

How do I write a state space model and how do you find the unknown parameters of phi, mu, and matrix A$_t,$ along with covariance matrices Q and R?

Consider a system process given by $x_t=-0.9x_{t-2}+z_t$,$t=1,2,…,n$ with observation $y_t=x_t+v_t$ where ${z_t}$ and ${v_t}$ are independent white noise with variances $σ^2$ and $σ_v^2$. Assume ...
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1answer
248 views

EM Algorithm seems to work, but Q is not monotonic. Possible reasons?

I have implemented Expectation maximization to fit some of the parameters of a linear Gaussian state space model using Kalman filtering / smoothing. The model is: $x(t) = Ax(t - 1) + w(t); w(t) \sim ...
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0answers
21 views

Correlated error terms in VAR and external observable AR as state equation

I ran into an estimation problem of a system that combines of a two-variable VAR(1) (entity level VAR(1)), and a AR(1) which represents the state. Can you help? Any suggestion would be appreciated. ...
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0answers
235 views

How to put an ARMA(2,2) model in state-space form

I am interested in an ARMA$(2,2)$ model with an additional input variable, which I want to put in state-space form. If $w_t$ is white noise, and $x_t$ is a known input, the model is given by: $$y_t ...
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1answer
47 views

Univariate Kalman filtering with factor in state-equation

I have a simple Kalman problem: how does one estimate the following local level univariate state-space model, but with some driving factor: ...
1
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1answer
189 views

State space models: Advantage of Stationary State Vector?

Consider a State Space Model, where the observed process is $Y_t$ $$ Y_t = B F_t + \epsilon_t \\ F_t = \Phi F_{t-1} + \nu_t $$ where the error terms are white noise. Later on, I want to compute the ...
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0answers
58 views

Need help conceptualizing MLE for stochastic processes?

I recently learned how to perform some Maximum-Likelihood Estimation, and thought I had a fair grasp of it. For example, for the normal distribution where both $\mu$ and $\sigma^2$ are unknown for ...
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1answer
59 views

prior for initial values of Kalman Filter

I'm studying Carter and Kohn's (1994) implementation of the Gibbs sampler for Bayesian analysis of state space models. In their paper, they assume the starting value, call it $\beta_0$, of the state ...
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0answers
134 views

Which model(s) can forecast a mixed-frequency multivariate dataset?

I'm looking to forecast a multivariate mixed-frequency(quarterly -- lower frequency and monthly -- higher frequency) with ragged-edge (be able to forecast when not all observations are present and re-...
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0answers
124 views

ARIMA and SARIMA state space form

I need to write down a program that place ARIMA(p,d,q) and SARIMA models in state space form, however I cannot figure out the composition of the system matrices. In the book of Koopman (pag. 54) the ...
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0answers
113 views

kalman filtering on time series with weekly trend

I'm trying to understand the application of kalman filtering on time series data and I find quite difficult to search good reference book on that. If I have a time series data, say a time series of ...
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0answers
41 views

Aggregating information and Bayesian information

Consider a binary random variable $\theta\in\{0,1\}$. I refer to this variable as "the state". Further assume that each possible state happens with equal probability (i.e., equal to $1/2$). I cannot ...
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0answers
279 views

Dynamic factor in statsmodels

I'm trying to use dynamic factor in statsmodels to estimate a model as following: $y_{1,t} = \alpha_1 f_t + N(0, \epsilon_1)\\ y_{2,t} = \alpha_2 f_{t-h} + N(0, \epsilon_2)\qquad h \text{ is unknown}...