Questions tagged [state-space-models]

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

Filter by
Sorted by
Tagged with
0 votes
0 answers
8 views

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 ...
user avatar
2 votes
0 answers
23 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 ...
user avatar
0 votes
0 answers
16 views

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 ...
user avatar
  • 1
0 votes
0 answers
15 views

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 ...
user avatar
0 votes
0 answers
25 views

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: ...
user avatar
0 votes
0 answers
6 views

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 ...
user avatar
0 votes
0 answers
16 views

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 ...
user avatar
  • 115
1 vote
0 answers
20 views

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 ...
user avatar
  • 11
0 votes
0 answers
33 views

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 $AR(1)$ ...
user avatar
  • 1
1 vote
0 answers
26 views

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} |...
user avatar
0 votes
0 answers
24 views

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,\...
user avatar
0 votes
0 answers
53 views

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 ...
user avatar
  • 1,125
0 votes
0 answers
29 views

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 ...
user avatar
0 votes
0 answers
18 views

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 ...
user avatar
0 votes
0 answers
24 views

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 ...
user avatar
2 votes
1 answer
48 views

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 ...
user avatar
1 vote
0 answers
19 views

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 ...
user avatar
1 vote
0 answers
33 views

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 ...
user avatar
  • 137
1 vote
0 answers
38 views

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 ...
user avatar
  • 1,700
0 votes
1 answer
45 views

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 ...
user avatar
1 vote
1 answer
116 views

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 ...
user avatar
3 votes
1 answer
147 views

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. ...
user avatar
0 votes
0 answers
62 views

Bayesian state space modelling using R with JAGs package

It is my first time to use Bayesian approach for state space modeling using r . I want to get the prediction error (using the state space model from Bayesian approach using JAGs) and the observed ...
user avatar
1 vote
0 answers
88 views

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 ...
user avatar
  • 11
1 vote
1 answer
98 views

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 ...
user avatar
  • 41
0 votes
0 answers
19 views

How to generate a state space model from data?

I am trying to identify a state space model from discrete time series data in Python using statsmodels library: ...
user avatar
  • 1
0 votes
0 answers
40 views

Next event prediction - approach

I have a problem that I do not know how to solve reasonably. I need predict date and amount of next (future) order of product. So my data looks like this: ...
user avatar
  • 101
0 votes
1 answer
21 views

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 ...
user avatar
  • 11
1 vote
0 answers
46 views

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}...
user avatar
  • 41
1 vote
1 answer
105 views

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 ...
user avatar
  • 41
1 vote
1 answer
29 views

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 ...
user avatar
  • 5,718
0 votes
1 answer
117 views

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?...
user avatar
  • 41
1 vote
0 answers
34 views

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, $$ a = M_1\ or \ M_2 $$ ...
user avatar
  • 11
1 vote
0 answers
12 views

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 ...
user avatar
0 votes
0 answers
48 views

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 ...
user avatar
0 votes
1 answer
35 views

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. ...
user avatar
2 votes
1 answer
171 views

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 ...
user avatar
  • 580
0 votes
1 answer
38 views

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: $$\...
user avatar
  • 1
1 vote
1 answer
215 views

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)...
user avatar
0 votes
0 answers
61 views

Issues with exogenous variable (dlm package R)

I would like to determine the parameters of the state space model \begin{align} \xi_{i+1}&= \widetilde{G}\xi_t+\phi x_t + V_{t+1} \\ R_{t}&= H^T\xi_t +\eta_t \end{align} using dlmMLE and then ...
user avatar
  • 41
1 vote
0 answers
134 views

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 ...
user avatar
  • 41
0 votes
0 answers
27 views

Recipe for a state-space model

What I am trying to do an interpolation with a state-space model. I have GDP quarter series and I am trying to obtain higher frequency values(monthly) using the information from Industrial Production ...
user avatar
1 vote
1 answer
161 views

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_{...
user avatar
2 votes
0 answers
75 views

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]) + \...
user avatar
0 votes
0 answers
58 views

How to estimate parameters of a state-space model when there are multiple time series as training data

I want to estimate the posterior distributions of the parameters of a state-space model implemented in Python using any library like Pystan, pymc, but I have multiple time series instead of a single ...
user avatar
  • 155
0 votes
1 answer
122 views

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 - \...
user avatar
2 votes
1 answer
67 views

Transforming/modelling a State-Space model as a Gaussian Process?

Is there a way to model, or represent/transform, a State-Space model as a Gaussian Process?
user avatar
0 votes
1 answer
67 views

Choleskly constraint in mlemodel in statsmodel

I want to constraint the off diagonal terms in the covariance matrix in a dynamic linear model. I tried using Cholesky method but it does not seem to converge. I am trying to fit a multivariate CAPM ...
user avatar
  • 151
2 votes
1 answer
48 views

Using eigendecomposition to transform state vector in linear Gaussian state space model

Paper: A Unifying Review of Linear Gaussian Models by Roweis & Ghahramani The generative model is the typical state space model written as \begin{align} \text{state transition equation: }{\bf x}_t ...
user avatar
3 votes
1 answer
75 views

Marginal Covariance of State Vector in a Linear Gaussian State Space Model

Paper: A Unifying Review of Linear Gaussian Models by Roweis & Ghahramani The generative model is the typical state space model written as \begin{align} \text{state transition equation: }{\bf x}_t ...
user avatar

1
2 3 4 5
7