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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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### Small noise of state process and filtering

Assume we have a linear state-space model: $$z_{k} = Hx_{k} + v_{k}\\ x_{k} = F x_{k-1}+ w_{k}.$$ We are interested in filtering, i.e. we aim to estimate $E[x_{n}|z_{0}, \dots, z_{n}]$. If the ...
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### How to evaluate state space model?

I have a state space model which is basically a Kalman filter. The parameters of the Kalman filter are unknown and are estimated from data using EM algorithm. After I get these parameters, what are ...
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### Fitting a Local Poisson model (Exponential Smoothing) [closed]

I am working through "Forecasting with Exponential Smoothing". I am stuck on exercise 16.4 on the part that states: The data set partx contains a history of ...
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### Predictions after SMC

I have a statistical model given by $$y_t\sim p(y_t|x_t, \theta)\\ x_t\sim p(x_t|x_{t-1},\theta)\\ \theta\sim p(\theta)$$ where $y$ is the only observed component. Using a sequential Monte Carlo ...
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### Outliers Kalman Filtering

This might not be the right place to ask this questions, but I figured it's more of a machine learning question. I am also asking on the pyro forum for brevity. I'm working with the simple extended ...
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### What is behind “forecast” in Eviews?

I have been trying to use state space models in order to represent some gestural data. Until now I have been using Eviews to to do all the dynamic forecasting part, so I was curious what is behind ...
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### Transition Matrix definition in State Space models using gestural data

I am trying to represent some gestural data (x,y,z from right hand & x,y,z from left hand) I am getting from sensors in a state space form, so as to predict the next x,y,z. Since statistics &...
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### What are the differences between Bayesian filters and adaptive filters?

I am learning about state estimation and I am having difficulty understanding the difference between Bayesian filters such as Kalman filter and particle filters compared to adaptive filters. According ...
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### Online learning from a Bayesian Perspective in a State-Space Model

I'm trying to learn how to do online learning from a Bayesian Perspective. My main interest is to use it for a State-Space model. However, any explanation/reference in a different context, which may ...
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I'm interested doing a dynamic factor model (DLM) similar to Doz, Giannone and Reichlin (2011) and Giannone, Reichlin and Small (2008). Moreover, I'm trying doing macroeconomic nowcasting model. In ...
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### how to model a state space with GARCH noise

I'm trying to model a state space model with GARCH noise and get stuck by the complexity of the equation. so the first equation is a observation equation and second one is a state equation where both ...
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### How to infer state space parameters from an LSTM model?

I'm attempting to create a state-space model by training my time series data with an LSTM. I'm hoping the LSTM will capture non-linear phenomenon as opposed to a linear state-space model. The only ...
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### How is the confidence metric of a state space model at a given state related to consumer demand for clickstream data?

I've been tasked to take over a project at my company where consumer demand for a given product is taken from the confidence metric of a given state of a state space model. The way it works is that ...
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### Equivalency between ARMAX and state-space model

I am trying to understand the equivalency between ARMAX and the state-space model. I have read articles/websites with different conclusions on this topic. Some people claim ARMAX and state-space model ...
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### Confidence intervals for state space models

i'm looking for on how to calculate the following ICs: smoothing, on-line filter and prediction on state space models. I'm not able to find any formula about them or any matlab command/class. Thanks....
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### Kalman filter parameter estimation

From what I've known about Kalman filter, it requires all the parameters of the underlying state space model. Say the state space model is: $$\xi_{t+1} = F\xi_t + v_{t+1}$$ $$y_t = H\xi_t + w_{t}$$ ...
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### Estimating a changing transit time between inputs and output

I work with a chemical process in which there is a time lag between the inputs (raw material quality and cooking parameters) and the output (final product quality). The problem is that the time lag ...
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### Eigenvalue decomposition of a covariance matrix using a fast Cholesky decomposition

Let $\mathbf{C}$ be a $n \times n$ covariance matrix and assume that the LDL' Cholesky decomposition can be obtained efficiently. Can we take advantage of this to obtain a fast eigenvalue ...
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### Updating State-Space Holt-Winters Model Latent Variables

I'm trying to update the level at time t of a state-space, additive damped Holt-Winters model with a given ...
I am estimating a state space of the following form $$Y_t= A X_t + \epsilon_t$$ $$X_{t+1} = B X_{t} + \sigma \sqrt{( a-X_t)(X_t-b)} \eta_t$$ Considering the variance of the state error is state ...