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

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4 views

Time-series variable normalization before using state-space models

I try to estimate a time-series with an SSM that I built. The problem is that model fit is not very good and I think normalizing variables might help. Both my dependent of some of my independent ...
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0answers
22 views

How to handle many-to-one data?

I'm trying a kaggle contest, just to improve my machine learning skills. The challenge I currently do involves many-to-one relational data. For instance, a person belongs to a municipality. A ...
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55 views

Estimating model's parameters from repeated measurement of a process, concept and application in R

I've asked a similar question here. A process is observed on various days, where each observation is a time series. for example the above figure shows 5 of these observations. My goal is to perform ...
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0answers
8 views

State Space ECM model

I want to estimate a TVP-ECM model in R. Is there a specific package in R that can handle TVP-ECM models? Thank you
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0answers
8 views

how can I use state space models for two dependent systems?

I use a space space model on my data and estimated its parameters via Kalman filtering. Now I have to expand it to two datasets. It means when you have two state space models and you want to see the ...
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1answer
43 views

On estimating ARIMA models on artificially made time series data

For each day, I observe my variable, y(t), for a period of 12 hours. In order to understand the data and make predictions, I want to put together these data and ...
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0answers
11 views

Extensions of bsts and CausalImpact to non-Gaussian exponential family distributions

The bsts and CausalImpact packages implement a state space time series model with an optional regularized regression component. ...
2
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0answers
42 views

Kalman filtering in [R] : FKF package and DLM

I am trying to implement a time varying state-space model in [R]. Model includes some exogenous variables that are part of the measurement and transition matrices. I tried multiple packages and my ...
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1answer
66 views

Why is forecasting of ARMA models performed by Kalman filter

What are the advantages of expressing an ARMA model as a state-space-model and do forecasting using a Kalman filter? This methodology is for example used in the SARIMAX implementation of ...
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1answer
43 views

Identifiability of a state space model (Dynamic Linear Model)

Take a general linear Gaussian state space model (SSM)(aka Dynamic Linear Model DLM): $X_{t+1}=FX_t + V_t$ $Y=HX_t+W_t$ $V_t \sim N(0,Q)$ $W_t \sim N(0,R)$ I am interested in the ...
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14 views

DLM with autocorrelated and non gaussian residuals

I quite new to state-space modelling, and I've been working on a DLM right now, using the dlm package (Petris, 2009). I want to forecast French car registrations since 1994 (till 2014), on a monthly ...
2
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4answers
98 views

DLM package, issues about specifying models with time-varying coefficient

I've been working on DLM package for the past few weeks. I've read the package manual and the paper written by Petris "dlm: an R package for Bayesian analysis of Dynamic Linear Models", but I am still ...
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0answers
85 views

State space model with intercept in transition equation and h-step forecast - FKF R

I think I found the solution myself but would need some verification by an expert. To see my solution you can skip the start and switch to the end of my question. My problem is now: How do I get a ...
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0answers
10 views

State-space model: measurement-driven steps?

I have a time series that seems to be well described by a univariate local level model (a changing bias in human visual perception, sampled at regular intervals). I have a hunch, however, that the ...
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0answers
45 views

Discrete sinusoidal to state space

I'm looking to apply an optimal LQR filter to a discrete signal of the form $x[n]=A \sin(\omega_0n + \phi)+ v[n]$ The amplitude $A$ and the phase $\phi$ are unknown variables I want to estimate ...
2
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0answers
22 views

Estimate latent states for a Bernoulli stace space model, when the latent states follow an AR(1) process

I am dealing with this model $$y_t|\alpha_t \sim Bernoulli \left( \frac{\exp (\alpha_t)}{ 1+ \exp(\alpha_t)} \right) $$ with $\alpha_t = \phi \alpha_{t-1} + \epsilon_t,$ where $\epsilon_t \sim ...
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0answers
80 views

How to represent an ARIMA(p,d,q) with dlm package in R? [closed]

I've been using DLM package for modeling my timeseries in state-space format, and then use Kalman Filter to get better 2 step-ahead forecasts. Even though I've read the vignette and parts of their ...
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0answers
102 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
43 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
56 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
58 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 ...
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2answers
59 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
73 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
125 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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40 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
41 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
123 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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0answers
62 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
88 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 ...
3
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2answers
209 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
75 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
31 views

Estimation of a system

Suppose we have a system that essentially evolves as follows: ...
5
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2answers
129 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
77 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 ...
1
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1answer
79 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
86 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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17 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: ...
6
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3answers
832 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) ...
0
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1answer
56 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
106 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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0answers
56 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
34 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) &= ...
1
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0answers
84 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 ...
0
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2answers
270 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
81 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 ...
3
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394 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
32 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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0answers
69 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
108 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 ...