Questions tagged [state-space-models]
It describes the probabilistic dependence between the latent state variable and the observed measurement.
1
vote
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
0
votes
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 ...
0
votes
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
votes
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 $...
0
votes
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 ...
0
votes
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}...
1
vote
0answers
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 $t \geq 0$
$$
\left\{
\begin{array}{c c l}
\text{d}{\boldsymbol{\...
1
vote
0answers
14 views
Are there any R code examples for estimating the state space vector in this case?
I couldn't make sure Whether the model I'm using is a local level model with multiplicative components (state vector $\times$ regressor vector) or a linear gaussian state-space model. And couldn't ...
1
vote
0answers
63 views
Unable to recover time varying AR1 parameter from State Space model
I am trying to do a Time varying parameters regression. The equation is as follows:
$y_t = a + b_t * x_{1t} + \epsilon_t$
Here a is fixed while $b_t$ is AR1.
My state space equations are :
There ...
0
votes
0answers
15 views
Linear regression of features inside a hidden Markov model?
I have an interesting little problem which I am trying to attack using HMMs.
First, as usual, I am trying to do time-series segmentation/classification using a HMM. But the input to my HMM has an ...
1
vote
1answer
66 views
State-space model with contemporaneous effects
I have the following system of equations:
$$
\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}
$$
where $y_t^{(1)}, y_t^{(2)}$ ...
1
vote
2answers
91 views
Kalman Filter Derivation - Shumway / Stoffer
I'm going through the proof of the Kalman filter equations in Shumway, Stoffer - Time Series Analysis and its applications. Could someone please tell me how equation (6.26) is justified? How can we ...
1
vote
1answer
144 views
Estimating State Space Model Parameters
I'm having a bit of difficulty estimating parameters in DLM in R and I was wondering if I could get a bit of help with it. I have a system of equations given as:
$p_{t} = m_{t} + s_{t}$
$m_{t} = m_{...
2
votes
1answer
81 views
State Space Model Form for Equations
I have a set of equations which I have to write in state space model form but unfortunately I'm having a bit of difficulty doing so. They are given as:
$y_{t} = x_{t} + z_{t}$
$x_{t} = x_{t-1} + w_{...
2
votes
1answer
106 views
Deriving a filter like a Kalman filter from a non-Gaussian state space model
Assume we specify a state space model as
$$Y_t = a X_t + W_t$$
and
$$X_{t+1} = b X_t + V_t$$
where $b,a \in R$, $E[W_t] = E[V_t] = 0 \quad \forall{t }$ and $W_t $ and $V_t$ are indipendent for ...
0
votes
0answers
60 views
Simple explanation of dynamic linear models
I'm looking for a really simple explanation of what a dynamic linear model is as I need to explain this to a non-technical audience. I have looked around for examples but they are very maths heavy.
I ...
0
votes
0answers
31 views
State space models with non stationary/unit root factors
state space model , I am trying to implement is as follows
$$ Y_t= CY + FF* X_t + Ve_t$$
$$(X_t-m0)= GG (X_{t-1}-m0) +W\eta_t$$
I am enforcing GG to be to be diagonal for the base case. I am getting ...
1
vote
1answer
31 views
Why is Qk not included in the cost function that is optimised by the Kalman filter?
Assume the following linear discrete system:
$x_k = Fx_{k-1} + w_{k-1}$ where $w_{k} \sim N(0, Q)$
$y_k = Hx_k + v_{k}$ where $v_{k} \sim N(0, R)$
One way to prove that the Kalman filter is optimal ...
-1
votes
2answers
37 views
Variance of a mixture of Normals with same $\sigma^2_i$
Let $Y\sim \sum^N_{i=1}\omega_iN(m_i,h^2 V)$.
The text I'm reading states that $Var(Y)=(1+h^2)V$, when $m_i=\theta_i$, where $\theta_i$ are draws taken from $P(\theta|D)$, and $V=Var(\theta|D)$
I ...
0
votes
1answer
71 views
Convert a state-space model with exogenous input to one without
I have a state space model of the form
\begin{align}
x_{t+1} &= Ax_t + Bu_t + w_t\\
y_t &= Cx_t + Du_t + v_t
\end{align}
where $u$ is the exogenous input. Also, $ w_t \sim N(0, Q)$ and $v_t \...
0
votes
0answers
33 views
state space implementation using DLM FKF
state space model , I am trying to implement is as follows
$$ 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 ...
0
votes
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
votes
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 ...
1
vote
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 ...
3
votes
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
votes
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 ...
0
votes
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 ...
1
vote
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. ...
2
votes
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-...
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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$$
...
2
votes
1answer
191 views
DLM representation of ARIMA models
I am working through example 3.2.6 in 'Dynamic linear models with R' by Petris. I have download the USA GDP data located here: http://definetti.uark.edu/dlm/
The example starts by estimating the ...
0
votes
1answer
31 views
State space model with third or more order trend
In state space model, a system model with first order trend is represented as
$$
x_{t} = x_{t-1} + e_{t},
$$
where $x_{t}$ is system model, $e_{t}$ is system noise.
Also, a system model with ...
0
votes
0answers
52 views
How does one approximate $\mu$ and $\sigma$ in an arithmetic Brownian motion using a Kalman filter?
My concern arises from the fact that in the following system:
$x_k = (\mu, \sigma)^T = x_{k-1}$
$Y_k = Y_{k-1} + \mu + \sigma Z_k \quad Z_k \sim N(0,1)$
that I cannot separate the states I want to ...
1
vote
1answer
69 views
How do I write a state space model and how do you find the unknown parameters of phi, mu, and matrix A$_t,$ along with covariance matrices Q and R?
Consider a system process given by $x_t=-0.9x_{t-2}+z_t$,$t=1,2,…,n$ with observation $y_t=x_t+v_t$ where ${z_t}$ and ${v_t}$ are independent white noise with variances $σ^2$ and $σ_v^2$.
Assume ...
1
vote
1answer
248 views
EM Algorithm seems to work, but Q is not monotonic. Possible reasons?
I have implemented Expectation maximization to fit some of the parameters of a linear Gaussian state space model using Kalman filtering / smoothing.
The model is:
$x(t) = Ax(t - 1) + w(t); w(t) \sim ...
0
votes
0answers
21 views
Correlated error terms in VAR and external observable AR as state equation
I ran into an estimation problem of a system that combines of a two-variable VAR(1) (entity level VAR(1)), and a AR(1) which represents the state. Can you help? Any suggestion would be appreciated.
...
1
vote
0answers
235 views
How to put an ARMA(2,2) model in state-space form
I am interested in an ARMA$(2,2)$ model with an additional input variable, which I want to put in state-space form. If $w_t$ is white noise, and $x_t$ is a known input, the model is given by:
$$y_t ...
1
vote
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
vote
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 ...
2
votes
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 ...
0
votes
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 ...
0
votes
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-...
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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}...
