Questions tagged [state-space-models]
It describes the probabilistic dependence between the latent state variable and the observed measurement.
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States in RNN: what if they are measured
A simple RNN will take the output and feed it back to a state variable. The next output is then the function of input and state.
Now imagine I want to use the "state" variable in RNN as an ...
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What is the difference between regression and state-space models?
I would like to know the differences between a regression model with autocorrelated errors and state space models (time series). When should each be used?
According to this lecture, regression (linear ...
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State-Space model with time-varying error in R
I am trying to estimate the following local level model in R:
$y_t = \theta_t + v_t$
$\theta_t = \theta_{t-1} + w_t$
where $y$ is the observable variable and $\theta$ is the latent variable. This ...
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Calculating probability from first principles (modelling real world complex events)
I am watching this video on YouTube, as part of a gentle refresher on prob and statistics (I have a Postgrad degree in the field, but haven't used it for a while - so I am not a complete beginner).
I ...
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How to retrieve in-sample predictions from BSTS Poisson model
Using the bsts R package to model a time series specifying a 'Poisson' family results in an error when trying to compute insample prediction errors: ...
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How to model 'switching' of covariate effects over time
Say we and a competitor each sell a similar product and we are interested in predicting how they will price their product in the future. There is decent variation day to day in the price of the ...
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Using ML in the prediction step of a kalman filter
I am trying to design a kalman filter to model an athlete's "skill". Each time they compete, we have a new data point - call it their "score". I am taking each score they receive ...
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State space model equation
I would appreciate your help on the following
I have a quadratic equation and need to write it in a state space format according to a model below. My equation is the following below, where T is the ...
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DLM package in R: No convergence
I am trying to decompose an observable time series $y$ into a permanent component $\bar{y}$ and a transitory component $\tilde{y}$.
In my model, the transitory component follows a stationary $AR(1)$ ...
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Computing mean of filtering and smoothing distributions from a particle filter
Suppose I have a model with latent states $x_1, x_2, \ldots x_T$ and observations $y_1, y_2, \ldots y_T$. I run a sequential monte carlo algorithm to give me the following approximation to $p(x_{1:T} |...
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Appendix A on Variational Gaussian Process State Space Model
On Frigola et al
in the Supplementary material A, equation (19) is:
$\prod_{t=1}^{T}p(\mathbf{f}_t|\mathbf{f}_{1:t-1},\mathbf{x}_{0:t-1},\mathbf{u})=\mathcal{N}(\mathbf{f}_{1:T}|\mathbf{K}_{0:T-1,\...
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Modelling irregularly sampled observations of a continuous time signal with a discrete state space model
I need to model time series whose observations are sampled at arbitrary points in time. By modelling, I mean that I would like to fit a generative (probabilistic) model that can approximately ...
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On the noiseless Kalman filter
Introduction
I've implemented a simple Kalman filter and I'm facing some difficulties into filtering out the noise of the measurements. If I set a small initial state covariance and a null process ...
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Configure exogenous variables in sarimax model to maximize target value
Given an sarimax model i want to forecast the future lets say 30 days configuring the exogenous variables so that we maximize the target variable y.
The domain of definition for the exogenous ...
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How to find state-space representation for an estimated HMM model in R
Take the toy (already estimated) HMM model below from the R package MSwM. How do I find a state-space representation for it? Put differently, what are the matrixes: ${G}_t,F_t,R_t,Q_t$ in the ...
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How to verify that a tentative state-space representation of an ARMA(1,1) process is valid
Brockwell & Davis example 9.1.2. show the state-space representation for {$Y_t$}, an ARMA(1,1) process. They claim that the 2 equations below are the observation equation and state equation ...
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Exogenous variables in state-space models (entering states versus entering observations)
From Shumway & Stoffer, Chapter 6 "State-Space Models" page 290: "...exogenous variables, or fixed inputs, may enter into states or into observations". Can somebody help me ...
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Random walk dynamics for coefficient bounded between -1 and 1
Suppose I have a linear state space model:
$y_t = \beta_tx_t + u_t \hspace{1cm} \mathcal{N(0,\sigma^2_u)}$
$\beta_t = \beta_{t-1} + \nu_t \hspace{1cm} \mathcal{N(0,\sigma^2_\nu)}$
For some reason I ...
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Where is a good place to start with (hidden) state-space models?
I'm interested in (hidden) state-space models. My language here might be poorly articulated as I'm quite new to this area of math. The topic of Kalman filters has come "across my desk" a ...
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Worst case error variance
I need to create an upper and lower bound for the error variance, in linear regression or otherwise (state space models etc.). One way is to bootstrap confidence intervals, but that can be very ...
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why should I transpose "coefficient vector" in linear regression?
I was reading a basic state-space model that looks like this (here, X is a vector of predictor variables):
My question is - why is the "coefficient vector" transposed in the regression ...
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Custom model using BSTS does not match with CausalImpact in R (please help!)
I am trying to match the results from using CausalImpact with those from using BSTS for a custom model. I followed exactly what the package instruction says but the results completely do not match.
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Bayesian state space modelling using R with JAGs package
It is my first time to use Bayesian approach for state space modeling using r . I want to get the prediction error (using the state space model from Bayesian approach using JAGs) and the observed ...
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Local linear trend model versus ARIMA
I was told that the local linear trend model also called 'basic structural model':
$\mu_t=\mu_{t-1}+\beta_{t-1}+\epsilon_t$
$\beta_t=\beta_{t-1}+\xi_t$
Is 'equivalent' to an ARIMA(0,1,1)
That's not ...
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Unknown parameter - augmenting state equation (Kalman filter)
First, we have a state space model with mean reversion and $\mu$ is unknown
$y(t )= F* x_t +e_t$
$x_t- \mu = G* (x_{t-1}-\mu) +n_t$
There is a option to add unknown parameters to the state vector and ...
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How to generate a state space model from data?
I am trying to identify a state space model from discrete time series data in Python using statsmodels library: ...
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Next event prediction - approach
I have a problem that I do not know how to solve reasonably. I need predict date and amount of next (future) order of product.
So my data looks like this:
...
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Is n-dimensional hypervolume different from n-dimensional state space?
Is there any difference between Hypervolumes (e.g. Blonder et al., 2014; Barros et al., 2016) and state spaces (sensu von Bertalanffy, 1972; e.g. Tett et al., 2013)? If so, what is it?
It seems that ...
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In-sample forecast accuracy of Beta (Kalman filter)
One can calculate time-varying betas (known from the CAPM) using the Kalman filter.
For example, one can calculate the in-sample forecast accuracy using the MAE.
$MAE = \frac{1}{T}\sum_{t=1}^T|\hat{R}...
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Understanding questions regarding the Kalman filter
I have a few questions about the Kalman filter in R (dlm package):
Given the function dlmFilter, there is the output time ...
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Can state-space models be used to solve this question?
Suppose there is a baseball stadium. The stadium has a food stand - let's assume that to make a purchase at the food stand, fans must purchase a ticket to watch the baseball game. This means that all ...
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Moving mean reverting model - Beta off the charts? (Kalman Filter)
I have implemented the moving mean reverting model with the FKF package, but unfortunately the beta as well as beta mean is way off as you can see in the chart. Is there anything I have not considered?...
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State-Space Model with categorical exogenous variables
I have a state-space model:
$$
x_{t+1} = A x_{t} + \alpha_{t} \\
y_{t+1} = B y_{t} + \beta_{t}
$$
The observation model is parameterized by a categorical exogenous variable, $$ a = M_1\ or \ M_2 $$
...
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dlmForecast error : "dlmForecast only works with constant models"
I have a dataset with intervention dummy variable to be incorporated inside the measurement equation (let's call Lambda)
I picture my measurement and state are as below :
measurement : Lambda + Et
...
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State-space model with mean-reverting coefficients
I am trying to estimate a state-space model with time-varying coefficients. I do plan to include multiple regressors in the model, but for simplicity let's assume that there is only one explanatory ...
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Online multivariate time series: imputation / forecasting of one of the channels with limited measurements
Problem:
Data: Online (continuous) stream of multivariate time series data (>5 channels)
The measurements from one of the channels (Channel F in example below) are irregular and (very) infrequent.
...
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Time Varying Coefficients vs Rolling Estimation
What are the practical differences for forecasting from fitting a model with time varying coefficients vs. estimating a model with fixed parameters over rolling windows? Intuitively it seems that ...
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Zero matrix as transition matrix for MA(1) process
While translating an MA(1) process $y_t=\epsilon_t+\phi\epsilon_{t-1} $with $\epsilon_{t}$~WN$(0,\sigma^2) $ to a space state model can I use the zero matrix as the transition matrix like this:
$$\...
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Exogenous variable in the state equation in statespace MLEmodel in statsmodels [closed]
I'm trying to fit the following model:
$y_t = \left[\begin{matrix} (1-w) & 1 & w \end{matrix}\right] \left[\begin{matrix} d_t \\ \mu_t \\ m_t \end{matrix}\right] + \mathcal{N}(0,\sigma_\eta^2)...
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Issues with exogenous variable (dlm package R)
I would like to determine the parameters of the state space model
\begin{align}
\xi_{i+1}&= \widetilde{G}\xi_t+\phi x_t + V_{t+1} \\
R_{t}&= H^T\xi_t +\eta_t
\end{align}
using dlmMLE and then ...
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Maximum likelihood parameter estimation for state space model (Kalman Filter)
it´s about a state space model that I want to run using the Kalman filter. However, certain parameters are unknown and must be estimated by the maximum likelihood method. The state space model is as ...
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Recipe for a state-space model
What I am trying to do an interpolation with a state-space model. I have GDP quarter series and I am trying to obtain higher frequency values(monthly) using the information from Industrial Production ...
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Applying outlier adjustment using student's t distribution in a state-space model
I'm exploring performing outlier adjustment in a state-space model by using student's $t$ distribution. The gist of the problem is formulated as follows:
$$ \begin{align*}
y_t^* &= u_t + o_t - o_{...
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State space model to invert moving average of AR1 process whose mean temporarily jumps up once
This is a follow up query of this question.
Here is the problem statement:
I have an AR1 process say x[t] whose mean jumps up in a given time period.
ie. $x[t]-\mu[t] = \phi (x[t-1] -\mu[t-1]) + \...
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How to estimate parameters of a state-space model when there are multiple time series as training data
I want to estimate the posterior distributions of the parameters of a state-space model implemented in Python using any library like Pystan, pymc, but I have multiple time series instead of a single ...
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Using a state space model to invert a moving average
Here is the problem :-
We have an AR(1) process, $x[t]$,
ie,
$(x[t] - \mu) = \phi(x[t-1]-\mu) + \epsilon_x[t] $
where $Var(\epsilon_x[t]) = \sigma_x^2$ and $Mean(\epsilon_x[t])=0$
ie. $x[t] = (\mu - \...
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Transforming/modelling a State-Space model as a Gaussian Process?
Is there a way to model, or represent/transform, a State-Space model as a Gaussian Process?
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Choleskly constraint in mlemodel in statsmodel
I want to constraint the off diagonal terms in the covariance matrix in a dynamic linear model. I tried using Cholesky method but it does not seem to converge.
I am trying to fit a multivariate CAPM ...
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Using eigendecomposition to transform state vector in linear Gaussian state space model
Paper: A Unifying Review of Linear Gaussian Models by Roweis & Ghahramani
The generative model is the typical state space model written as
\begin{align}
\text{state transition equation: }{\bf x}_t ...
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Marginal Covariance of State Vector in a Linear Gaussian State Space Model
Paper: A Unifying Review of Linear Gaussian Models by Roweis & Ghahramani
The generative model is the typical state space model written as
\begin{align}
\text{state transition equation: }{\bf x}_t ...
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