Questions tagged [state-space-models]

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

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Parameters in mlemodel in statsmodel

I am trying to run a TVP-VAR on statsmodel for a big data, but seems to run in a problem when I am trying to validate the vector matrix and the vector shape. Particularly, in the start and the update ...
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How do we identify parameters in this simple model?

Consider the following model: $$ y_{it}=\nu_{it}+\epsilon_{it}$$ $$\nu_{it}=\rho \nu_{it-1}+\zeta_{it}$$ Where $y_{it}$ is the income for $i$ at time $t$. $\epsilon_{it}$ is the idiosyncratic income ...
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State space models in python statsmodels: including lag state innovation in observation equation

I am trying to fit the following state space model via the (excellent and highly useful) statsmodels state-space module. The model is a standard local level model but where last period's innovation ...
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Fitting TVP-VAR statespace mlemodel in statsmodel

1 Thanks to everyone in advance for their time! I am trying to run a TVP-VAR for a panel in the statespace mlemodels in statsmodel. I get an error while trying to fit the model ...
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Full conditional distribution (for Gibbs sampling) when model contains a logical node

I'm working on a time series model using a Bayesian implementation in JAGS. The simplest version of my model is an integrated random walk. The heart of the model is this: $y_t \sim N(\mu_t, \sigma)$ ...
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Slice sampling in Particle Gibbs with Ancestral Sampling

Bear with me as I am not from statistical background. My question is about the implementation of PGAS algorithm as given in Lindsten et. al 2014 concerning sampling in state-space models. The two ...
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Subspace method fails at identifying parameters in a state space system

I am trying to infer the parameters of a linear multivariate time-invariant state space system using a subspace method. However, the inferred parameters do not match the ground-truth parameters used ...
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statespace mlemodel in statsmodel does not converge

I'm trying to estimate the following state-space model: $$ y_{t} = \begin{bmatrix}1& 1 \end{bmatrix}\begin{bmatrix}\mu_{t}\\v_{t}\end{bmatrix} + \epsilon_{t},\quad \epsilon_{t}\sim N(0,\sigma_{\...
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TVP-VAR fails statespace.MLEModel

I am trying to run a TVP-VAR for a panel in python using statsmodels. I am using the site example, trying to adopt it in my model. Data are from 1945-2020 for 50 countries Furthermore, I am getting ...
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Kalman filter for forced system

I have a rather fundamental question regarding Kalman filters in "real life". As far as I know, Kalman filters (in particular as predictors) are used in many technological applications. I've ...
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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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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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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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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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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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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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