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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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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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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