Questions tagged [state-space-models]
It describes the probabilistic dependence between the latent state variable and the observed measurement.
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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 ...
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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 ...
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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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How do I calculate the standard error of Kalman Filter parameter estimates?
I am trying to implement the Schwartz-Smith (2000) commodity pricing model from the paper Short-term variations and long-term dynamics in commodity prices
The model is estimated using the Kalman ...
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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:"
$$ X_t = \mu_t + n_t $$
$$ \...
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Panel State Space Model in statespace.mlemodel in stats models
I am trying to write a custom statespace.mlemodel for panel data. I have 2 observation equations and 3 state equations.
$$
y_{1,i,t+1} = \alpha + x_{1,i,t} + \phi_{1,1} x_{2,i,t} + \phi_{1,2} x_{3,i,...
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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^...
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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 ...
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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 ...
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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 ...
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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 ...
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Estimating a model with two unobserved components that has measurement equation, signal equations and three transition equations
I have a dataset containing CPI inflation, 10 year breakeven rate, output gap, relative import price inflation, 2-year breakeven rate, 2-year firm inflation expectations, 2 year household inflation ...
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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 \...
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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 ...
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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 ...
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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{...
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state space models implementation in R
I'm trying to implement a state space model in R with daily data.
Is there any package to do this in R? I haven't been able to find one.
A little bit of context:
I need a model for forecasting gas ...
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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, ...
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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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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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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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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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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, $\mathbf X$ is a vector of predictor variables):
$$
\begin{align}
&(1) \quad y_t = \mu_t + \tau_t + \lambda_t + \epsilon_t, \...
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