# Questions tagged [state-space-models]

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

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### State space models and Kalman Filter

I have the following model specification: $y_t = \mu_t + v_t,$ $\mu_{t+1|t} = \phi \, \mu_{t|t-1} + k\, v_t$ where v_t= y_t - mu_{t|t-1}, v_t|F_{t-1} ~ tv(0, sigma^2). I was asked to provide the ...
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### Ways to parametrise a positive parameter

I am working with a differentiable state-space model involving a noise variance term $\sigma^2$ which I want to parametrise based on some features, e.g. $\sigma^2 = g(X\beta) > 0$, wherer $\beta$ ...
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### What if there is only one measurement equation containing two (or more) state variables while there are two unobservable state variables in a model?

I am learning Kalman Filter and ran into a question about the case in which only one signal is available. It is commonly assumed that the number of states equals the number of observations (signals) ...
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### Errors and residuals in simple exponential smoothing (state space form) in FPP textbook

I am reading Hyndman & Athanasopoulos "Forecasting: Principles and Practice" 2nd edition (FPP2). (I am aware that 3rd edition exists.) In the chapter about exponential smoothing, section ...
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### How to incorporate sources of observational error in state space model?

I’m learning about state space models. I understand the concept of a latent process that is unobserved, and a noisy set of observed data that we can use to estimate the latent process. I am trying to ...
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### Regressing time series of continuous proportions Y(invested in different buckets) against X (prices) variables

I am not sure of what model need to be applied in my case. So my goal is to model the below data. I have the monthly deposits data from 2001 till 2024 for this analysis. Each customer can invest in ...
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### Does this state space model make sense?

I'm working on a problem, Consider that a times series $\{y_t\}$ is generated from an $\text{ARIMA}(1,1,1)$ model, so that $$y_t-y_{t-1}=\alpha(y_{t-1}-y_{t-2})+\epsilon_t+\gamma\epsilon_{t-1},$$ ...
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I have a large number of MARSS dynamic factor analysis models that, based on AICc, are all competitive for the 'best' model. Is there a way to implement a model averaging process so that I can extract ...
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### Repeated measures of multiple time series processes

I am struggling with a comparison of temporal processes, which are observed in several time series. The problem is as follows: Suppose there are some semi-experimental conditions, with several ...
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### Bivariate State Space Model Using R Package DLM. Modelling correlation

I am trying to estimate a bivariate dynamic linear model. The data are public sector wages and private sector wages in the UK which we can assume are highly correlated. That is, a seemingly unrelated ...
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### Determine the parameters of a particle filter that best fit observations

I am wondering is there any established framework to optimize the parameter $\lambda$ of a particle filter such that $p(O|\lambda)$ is maximized, where $O$ is the observation sequence. For HMM and ...
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### arma confusion in R

Say I've got some AR(1) data from the model $x_t = .9 x_{t-1} + \epsilon_t$: dta <- arima.sim(model = list(ar=.9), n = 1000) I can instantiate an ...
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### What does it mean to have an observation variance of zero when fitting a model using StructTS in R?

I'm using the StructTS() function in R to fit 50 structural time series models (state-space models) on 50 univariate time series. I'm using the "trend" ...
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### Block sampling hidden state using forward algorithm only

In a hidden Markov model, I can't get my mind around why I can't sample the full hidden state $\vec x$ using only a forward sampling algorithm. Let $\vec y$ be the observed data and $\theta$ the model ...
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### Why should we need the acf of a series to define its joint distribution?

I'm working on an unassessed course problem, Consider the time series $y_t$ generated by the state space model with $x_t=1$, $F_t=\lambda$, $\sigma_2$, $Z_t=Z$, where the variances $\sigma^2,Z$ and ...
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### Identification of Non-Gaussian State Space Model

The following paper details necessary assumptions in order to have a non-gaussian state-space model be identifiable (see A1-A5); 'A General Linear Non-Gaussian State-Space Model: Identifiability, ...
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### What can you do with quantified uncertainty in latent variable time-series models?

Uncertainty quantification in latent variable models is a topic I am interested in, but I am struggling to grasp the difference between what you can do with quantified parameter uncertainty and ...
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### How to handle exact diffuse initialization of a Kalman filter?

This is partially a coding question so I hope I'm on the right platform for this. I am fitting a dynamic factor model using the state space framework. I don't know the initial distribution of the ...
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### ARIMA, VAR and State Space Model (SSM) forecasting comparison

I am trying to compare the asset price forecasting abilities of SSMs with ARIMA and VAR models. To keep it brief, this is the plan that I am following: Collect multivariate data Perform ADF ...
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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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### 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 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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