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

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24 views

How to use a Hidden Markov Model to detect state in a time series?

Questions Am I right in assuming that the emission probabilities will not be following a gaussian distribution for my particular problem? Obviously, I will need to train the model for state ...
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1answer
21 views

Exponential smoothing state space model - stationary required?

I came across with the Exponential smoothing state space model for time series forecasting. My question is if it does require that the time series is stationary? Is there any paper that explicitly ...
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1answer
37 views

Jags - estimates are same as true values of y?

Lets say I have the following state space model: $y_t = \beta_t x_t + \epsilon_t$ $\beta_{t+1} = \mu_t + \beta_t \eta_t$ $\mu_{t+1} = \mu_t + \omega_t$ All my true values for $y$ are known, but I ...
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1answer
23 views

Can Jags be used to fit classical inference state space models?

Can Jags be used to fit classical inference state space models (that is without using a Bayesian approach by specifying a prior)? To be fully clear: can I estimate a state space model such as the ...
4
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0answers
127 views

T distribution state space models

I want to estimate the following state space model: $y_t = \beta_{1,t} + \beta_{2,t} x_t + \epsilon_t$, $\beta_{1,t+1} = \beta_{1,t} + \eta_t$, $\beta_{2,t+1} = \beta_{2,t} + \omega_t$, ...
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1answer
15 views

Augmenting Kalman filter with parameter — what does the initial value mean?

It is a fairly standard trick to augment a Kalman Filter with unknown parameters and to propagate them forth with zero error to estimate them. I was wondering if anyone could tell me what the ...
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1answer
17 views

State space models in dlm package - how to add a non time-varying constant?

I am trying to compare the following two models: \begin{align} y_t &= \beta_{0,t} + \beta_{1,t} x_{t} + \epsilon_t\\ \beta_{1, t+1} &= \beta_{1,t} + \eta_t\\ \beta_{0, t+1} &= ...
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2answers
66 views

How to specify a state space model with cycle in this case?

I am trying to specify a state space model for the dependent variable from this graph. As you can see, there clearly seems to be cyclical behaviour. Therefore, I tried to specify the following state ...
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0answers
26 views

Doubt in state space representation for time series model

$y$ is scalar observations and so C will be a 1x2 matrix. I want to represent the following model as a state space representation so as to estimate the hidden states from the noisy observations $y$ ...
2
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1answer
35 views

How does this expected value translate into a conditional variance?

I'm working with a simple local level model in a textbook \begin{align} y_t &= \alpha_t + \epsilon_t, \qquad \epsilon_t \sim N(0, \sigma_\epsilon^2) \\ \alpha_{t+1} &= \alpha_t + \eta_t, ...
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1answer
91 views

Information about Kalman Filter

I was intending to develop a paper work using Kalman Filter, but I have a few questions about this subject: What are the main differences between a simple AR Model and Kalman Filter? Would it be at ...
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39 views

State Space model question

I am looking for some help with estimating Space state model of this form: $r_{t} = r^{*}_{t} + \pi + \varepsilon_{1}$ $R_{t}= r^{*}_{t} + \alpha + \pi + \varepsilon_{2}$ $r^{*}_{t} = ...
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0answers
35 views

Comparison between ARIMA and ETS models

I have a time series that I'm fitting models to, using R. I have chosen an ARIMA model based on minimising the AIC_C values. The ETS model (ets()) was chosen based on minimising the model accuracy ...
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2answers
173 views

Which econometric indices are best for macroeconomic variables?

I want to test index models that are applicable to macroeconomic data to test my hypothesis in R or some other statistical software (I have most of them). The properties of most of the macroeconomic ...
3
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1answer
62 views

How do you simulate two correlated AR(p) time series?

I would be interested in the mathematical framework plus code in R if possible. Basically I want to find out the parameters of the two AR(p) models if I already specificed a certain cross-correlation ...
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1answer
29 views

Estimation of a system

Suppose we have a system that essentially evolves as follows: ...
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2answers
98 views

What's the model representation for the first difference of a local level model?

This is my first exercise for space state models and I've a few questions I'd need to resolve before I actually start doing the exercise. Unfortunately, I'm self teaching (I have no professor to ask) ...
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0answers
39 views

What state-space representation of VARMA is commonly used for fitting

What state-space representation of VARMA is commonly used for fitting? Is Kalman filter + MLE approach used for fitting VARMA model as a common practice? Does the choice of which state-space ...
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1answer
65 views

How to Determine whether Simulation Draws are Correct

I have implemented algorithm 1 and 2 in this paper http://www.lse.ac.uk/statistics/documents/researchreport61.pdf for the analysis/simulation hidden states for some time series. The reason why I am ...
4
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1answer
74 views

State space model with regression effects

I'm trying to show the following (exercise 3.11.4 from Durbin and Koopman (2012)): Show that the state space model defined by $$ y_t=X_t\beta+Z_t\alpha_t+\epsilon_t\\ ...
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0answers
15 views

Calculate probability distribution $p\left(\left.X_{1:T}\right|Z_{1:T},y_{1:T}\right)$ in linear- non-Gaussian state space model

I have a linear, non-Gaussian state space model. Observation equation: $y_{t}=a+bX_{t}+cZ_{t}+\epsilon_{t}$ $\,\,\,\,$ $\epsilon_{t}\sim\mathcal{N}\left(0,\omega^{2}\right)$ Transition equations: ...
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3answers
233 views

How to interpret PCA on time-series data?

I am trying to understand the use of PCA in a recent journal article titled "Mapping brain activity at scale with cluster computing" Freeman et al., 2014 (free pdf available on the lab website). They ...
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0answers
15 views

Is Kemeny constant linear?

I have some results from analyzing music that were surprising to me, and I want to make sure I understand what I'm seeing. I have parsed a MIDI file of a Beethoven Symphony (No. 7 second movement) ...
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1answer
47 views

Backward message passing in variational Bayesian inference

I have come across in a research paper that, I do understand the logic. But the paper has't mentioned about the way of updating $\eta_{t}$. When I asked from the authors they said when we equate ...
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72 views

Specifying a State Space Model with the MARSS package

I would like to use the state space technique outlined in the paper by Mokinskia et al. (https://www.american.edu/cas/economics/research/upload/2013-4.pdf) to estimate time varying and asymmetric ...
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44 views

Calculate standard error in state space model in R

I am estimating a DFM in state space form in R. I have used the function spg from the package BB (optim was not working) and dlm to optimize so now I have the parameters of the filter. I now would ...
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1answer
32 views

Data transformation

I was writing with a question regarding a time-varying state space model of the form: \begin{align} y(t) &= \mu_1(t) + A(t)x(t) + v(t); &v(t) &\sim (0, R(t)) \\ x(t) &= ...
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72 views

State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure ...
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2answers
201 views

How do I replicate these simple state space models from Commandeur's book in Stata?

I'm working through the book An introduction to state space time series analysis by Commandeur and Koopman, and I want to replicate a few of the simple models in Stata 13.1. The two related models I'm ...
0
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1answer
67 views

A Kalman Filter for estimating z-scores?

I have been struggling to fit the following problem into a linear state space model for a Kalman Filter (KF). I'm having a hard time seeing what I'm doing wrong. I suspect I'm violating some law of KF ...
2
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0answers
276 views

Forward Filtering Backwards Sampling (FFBS) and Look-Ahead Bias

Assumptions / Context: Let's assume that I have data that can be modeled as a dynamic linear model. To estimate the parameters (e.g., covariance matrix of the state/system equation), I use a Gibbs ...
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1answer
31 views

State-space model with strict positive values

I've got a random process of positive observations. I've built a state space model (following an ARMA(1,3) structure), found the parameters that fit the process observations through log-likelihood ...
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27 views

forecasts ahead of t+1 in time-varying linear state space models

When the matrices in the model are constant, then performing forecasts is straight-forward. However, when using a time-varying model like dynamic regression I'm not sure how to proceed since we don't ...
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0answers
51 views

understand forecasts in linear state space models

The Kalman Filter provides the one-step-ahead forecasts within the recursions. We start estimating the (unkown) variance of the parameters for instance through MCMC ...
0
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1answer
90 views

Kalman filter conceptual question

I'm using the function dlmGibbsDIG (Gibbs sampler) in the dlmpackage from R to estimate the unknown variances. The output are ...
0
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0answers
51 views

Identifiability for time invariant state space models

Kevin Murphy's Kalman Filter toolbox (for Matlab) contains an example where it's the fact that the state space system in not identifiable causes problems. I include the example in it's entirety but ...
2
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1answer
147 views

Simulating state space model with AR(1) dynamics

I asked a question similar to this previously: Check that state space model implemented correctly However I think I have a better handle on it now and want to re-ask it: I simply want to simulate ...
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45 views

Check that state space model implemented correctly

I want to simulate data from the following model: $\textbf{z}_k=\textbf{H}\textbf{x}_k+\textbf{v}_k$ $\textbf{v}_k \sim N(\textbf{0},\textbf{R})$ $\textbf{H}$ does not change over time $\textbf{x}$ ...
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2answers
135 views

DLM seasonality with daily data

I have a series of daily temperatures and have fitted a model using the function dlmModTrig of the package dlm in R which uses ...
0
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0answers
44 views

How can I transform Ornstein-Uhlenbeck model into state space form?

As I say in the subject, How can I put the model $d x_t = \eta\, (\overline{x} - x_t)\,d t + \sigma\, x_t\,d W_t$ into state space form? I mean, which are the observation and transition matrices?
2
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1answer
77 views

Correlated state-space models

I'm struggling with Reinsel's book "Elements of Multivariate Time Series Analysis," because I thought that it would be a good idea to switch from Vector ARMA to state-space representations; ...
1
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1answer
147 views

Constants in a DLM Model R

Good afternoon, I am attempting to fit a state space model of the form: $$ (S_t- \mu) = G*(S_{t-1} - \mu) + E_t $$ $$ Y = F*S_t + v_t $$ Where $Y$ is nx1, $G$ is 3x3, $S_t$ is 3x1, $\mu$ is 3x1, and ...
0
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1answer
84 views

Kalman filter and Box-Cox

I'm interested in wind forecasting, which I have analyzed over some time by means of ARMA methods. Now I've being reading about Kalman filtering. Kalman filter is optimal when Gaussian assumption can ...
2
votes
1answer
39 views

probability definition of time and place event help in definition representation

I have a probability question: How can I represent the probability of an event occurring at a specific {time,place}? How are the time and place represented? Example: I want to represent the ...
2
votes
1answer
153 views

Random walk with drift in dynamic linear model

Suppose I have a dynamic linear model as defined in the dlm-package for R, see Petris 2009. $y_t = F_t θ_t + ν_t, ν_t$~$N(0,V_t)$ $θ_t = G_t ...
2
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0answers
47 views

Gibbs sampler for local linear trend model

Question: Consider the local linear trend model given by: \begin{align*} y_t = \mu_t + \tau \varepsilon_t \ \cdots \ \text{Observation equation} \\ \mu_{t+1} = \phi \mu_t + \eta_t \ \cdots \ ...
2
votes
1answer
283 views

How does JAGS deal with state space models?

I am trying to use JAGS to deal with the following multivariate state space model. $Y_t=X_t\theta_t+\epsilon_t$ $\theta_t=\theta_{t-1}+\nu_t$ JAGS code is neat but JAGS is running too slow when I ...
6
votes
1answer
329 views

Explaining Kalman filters in state space models

What are the steps involved in the use of Kalman filters in state space models? I have seen a couple of different formulations, but I'm not sure about the details. For example, Cowpertwait starts ...
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0answers
191 views

Weighting data sources in a bayesian model (BUGS)

I use a state space model to fit observations to a population dynamic model (using the BUGS language). In the "state" part, the dynamic model create a new "state" of the population (i.e. size and ...
1
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2answers
117 views

How do I perform a multi-state decomposition with interaction effects?

I am trying to perform a decomposition with interaction effects. This paper provides a solution for n-factors where each factor has a binary state (see section 2). I have a problem with 2 factors, ...