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

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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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25 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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23 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
152 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
52 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
28 views

Estimation of a system

Suppose we have a system that essentially evolves as follows: ...
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2answers
79 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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26 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
58 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 ...
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1answer
61 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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14 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
182 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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11 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
42 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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0answers
55 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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39 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
30 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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68 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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1answer
140 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 ...
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1answer
60 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 ...
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229 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
28 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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49 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 ...
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1answer
85 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 ...
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48 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 ...
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1answer
130 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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40 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
112 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 ...
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35 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
74 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; ...
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1answer
124 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 ...
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79 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
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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
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1answer
139 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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42 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
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1answer
237 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
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1answer
297 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
182 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 ...
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2answers
113 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, ...
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78 views

Sensible Transformations of Economic Indices like CFNAI and ADSBCI in Time Series Analysis

I am trying to fit an unobserved components model for revenue and transactions for a firm where I also use some exogenous variables that capture economic conditions. The UCM decomposes a time series ...
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45 views

Introducing observation errors in jags code

I want to introduce observations errors around my data in Jags, but I face some trouble coding it without having a double definition error on node Y3 So far I have : ...
6
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1answer
949 views

Dynamic factor analysis vs state space model

The MARSS package in R offers function for dynamic factor analysis. In this package, the dynamic factor model is written as a special form of state space model and they assume the common trends follow ...
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0answers
77 views

Rao-Blackwellising state space for a (marginalised) particle filter

I am starting to look at particle filtering for a problem that I have. In particular, I would like to reduce the dimensionality of the particles. The model that I have is able to be partitioned. ...
2
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0answers
345 views

State space representation using KFAS package

I am using KFAS package for R. You can run install.packages("KFAS") library(KFAS) ?regSSM ...
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0answers
130 views

Poisson State Space with AR(1) latent process

I have been trying to use sspir R package to estimate the following Poisson model: $Y_{t}\sim Po(\exp(\lambda_{t}));$ such that $\lambda_{t}=X_{t}\beta +\gamma_{t}$ and ...
2
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2answers
344 views

Exogenous variables in dlm package

I have been trying to estimate state space models using dlm package in R. The problem is that the model I am estimating requires inclusion of a few exogenous variables. I still can't figure out how to ...
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132 views

Criticism, please: simplifying state space model

As a little experiment, I am extending a nice, interpretable AR/MA relationship between a security $r$ that is variably influenced by the previous $k$ time points over another security $f$. These ...
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71 views

Building artificial state space model from noise-less data

I have a discrete time stochastic process, where at each time the state of the system $X_t$ is given by: $$ X_t = f_\theta(X_{t-1},\epsilon_t), \; \; \text{for} \; t = 1,\dots,T $$ and, for example, ...
3
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2answers
703 views

Confidence intervals for exponential smoothing

I'm using exponential smoothing (Brown's method) for forecasting. The forecast can be calculated for one or more steps (time intervals). Is there any way to calculate confidence intervals for such ...