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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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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 ...
Richard Hardy's user avatar
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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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model averaging with MARSS

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 ...
tnt's user avatar
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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 ...
Sean's user avatar
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Bayesian estimation of nonlinear state space model using Gibbs Sampler

I want to estimate a state space model that looks like this: $y_t = exp(\beta_t)x_t + \varepsilon_t \hspace{1cm} \varepsilon_t \sim \mathcal{N}(0, \sigma^2_{\varepsilon})$ $\beta_t = \rho\beta_{t-1} +...
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What kind of series is this? Time series Model Choice

I am trying to model a series (mainly as self-education, as a way of deepening my time series knowledge). The series is percentage growth in GDP per capita for the United States, taken from the World ...
Lindsay's user avatar
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Looking for books and/or other resources for Multivariate Statistics for Optimal Estimation

I was trying to familiarize myself with state estimation theory by going through Optimal State Estimation and I realized I don't have the required background in Multiple Random Variables and ...
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Finding functional forms and state space in a state-space model

Let's say that we have a time series: $$\{y_i\}_{i=0}^{n-1}, y_i \in \mathcal{Y} \subseteq \mathbb{R}^m, m \in \mathbb{N}_1$$ that we would like to model with some sort of state-space model: $$x_i = f(...
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Local linear trend-exponential smoothing duality with non-Gaussian likelihood?

Say we have the following state space/structural time series model: $$ y_t \mid \mu, \sigma \sim \text{Normal(} \mu = \mu_t, \sigma^2_\varepsilon) \\ \mu_{t+1} = \mu_t + \eta_t $$ where $$ \eta_t \sim ...
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Kalman filter + MCMC vs pure MCMC for bayesian dynamic linear(state space) models

I have heard that you can use both kalman filter integrated with MCMC to estimate bayesian state space models, i have also heard that you can use pure MCMC to estimate bayesian state space models. Why ...
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timevarying effects in regression vs state space models

Consider the following regression model: $z_t = \alpha + trend_t + seasonality_t + \epsilon$ $\alpha \sim HalfNormal(1)$, $trend_t = \mu t$ where as $\mu \sim Normal(0, 1)$ $seasonality_t = \sum_k^K [\...
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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 ...
Lindsay's user avatar
3 votes
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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 ...
Taylor's user avatar
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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 ...
J. Zeitouni's user avatar
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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, ...
PatrickStar's user avatar
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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 ...
kb563's user avatar
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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 ...
eork's user avatar
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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 ...
bullfighter's user avatar
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Problem from Chatfield and Xing on State-Space Model

Chapter 10, Problem 2 from The Analysis of Time Series by Chatfield and Xing: The problem says, "Consider the following special case of the linear growth model:" $$ X_t = \mu_t + n_t $$ $$ \...
Barry's user avatar
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Comparison of two models with different number of parameters

I want to compare two models, which has different number of parameters. The first model is Arbitrage free Nelson-Siegel model, which has the following equation: $y_{t}(\tau )=X_{1,t}+X_{2,t}(\frac{1-e^...
Shelley's user avatar
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Do we need to propagate state covariance matrix 'P' during missing observations in the Extended Kalman Filter?

Basically as the title says: in a scenario, we have missing observations where the entire state vector is unknown for consecutive time steps. Do we just run through the prediction section of the ...
user383687's user avatar
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BSTS package cannot capture seasons in simulated data

I am self-learning about structural time series, and for me the best way to understand topic is to simulate the data myself. I want to simulate a time series of local level model with seasonal ...
PK1998's user avatar
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Normality of data used to estimate significance of ARIMA parameters?

Does significance testing (p-value, 95% prediction interval of a forecast, etc.) of an ARIMA model require time series data to be normally distributed? As in, according to the tests used to assess ...
Eric's user avatar
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Recurrent neural networks vs. State space models

I'm trying to understand the differences between RNNs and State Space Models (SSMs). I know that SSMs can take on different definitions depending on who you ask, but here I define it as in Learning ...
paul's user avatar
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How can I re-write the expectation for a linear quadratic Gaussian problem?

Let $x_0 \sim N(\mu_{x_0},\Sigma_{x_0})$, where $\mu_{x_0} \in \mathbb R^n$ and $\Sigma_{x_0} \in \mathbb R^{n \times n}$. Then, let $$ y_0 = Cx_0 + v_0 $$ where $C \in \mathbb R^{n \times n}, v_0 \...
mhdadk's user avatar
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State Space with Space Lags in R (dlm, MARSS or anything else)

** Edited to reflect on some first comments ** I am trying to estimate a state space model which does a kind of disaggregation. In particular, I am interested in estimating high-frequency unobserved ...
Carl Dhreiner's user avatar
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How to use Forwards algorithm for HMM with Continuous Observation model $P(y|z_t=k)$

I have implemented a Forwards-Backwards algorithm for discrete latents HMM given the observed distribution matrix $B$. Now if the observed distribution matrix is a Gaussian instead of finite ...
wd violet's user avatar
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Relationship Between "ARIMA" and "State Space"

I attended a "Lunch Seminar" hosted by the Engineering Faculty in my school where they showed how Time Series Models are being used in different Electrical Engineering projects. Some of the ...
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How to smoothen state probabilistic time series?

I have an array of where each columns represents the probability of being in a certain state and rows represent time indexes. Each one of the rows sum up to one (we always are in one state). \begin{...
AlphaX's user avatar
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State space model parameterized by a neural network

For the sake of argument, assume the following simple state-space model: Transition model: $x_{t}=a\cdot x_{t-1}+\epsilon_t$ Measurement model: $y_t=f(x_t)+\delta_t$ Assume $x_t$ and $y_t$ are 1D, ...
Tomas's user avatar
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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 ...
Ludwig Gershwin's user avatar
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428 views

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 ...
jb1966's user avatar
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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 ...
David K's user avatar
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2 votes
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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 ...
Zero's user avatar
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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 ...
Camille Gontier's user avatar
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174 views

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_{\...
bw92's user avatar
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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 ...
David K's user avatar
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3 votes
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315 views

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 ...
nuggetEf's user avatar
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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 ...
HelenA's user avatar
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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} |...
snickerdoodles777's user avatar
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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 ...
ColorStatistics's user avatar

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