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13 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
23 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
30 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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1answer
78 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
38 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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0answers
56 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
21 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
24 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
37 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
59 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
33 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
86 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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0answers
31 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
71 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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0answers
25 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?
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1answer
50 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
89 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
59 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
37 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
120 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
31 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 \ ...
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0answers
63 views

A question on making prediciton from state space model

I am trying to use JAGS to make prediction from a state space model. I use JAGS to estimate parameters in the model and make prediction. I plot the hist graph for a.new and r.new, the graph for r.new ...
2
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1answer
144 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 ...
5
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1answer
243 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
108 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
97 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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0answers
76 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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0answers
38 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
632 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 ...
2
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0answers
66 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
273 views

State space representation using KFAS package

I am using KFAS package for R. You can run install.packages("KFAS") library(KFAS) ?regSSM ...
1
vote
0answers
114 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
293 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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0answers
117 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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0answers
65 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
555 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 ...
0
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1answer
226 views

Assumption of Gaussian distribution of acceleration

I have a data set consisting of noisy position values of a trajectory of a human hand. I want to estimate a generative model of these trajectories, and the obvious choice is a Kalman Filter/linear ...
3
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1answer
765 views

Estimating State Space Model in R with MARSS package and shared parameters between Q and R

I am trying to estimate the following unobserved components model using the MARSS package $y_t = \mu_t + \varepsilon_t $ $\mu_t = \mu_{t-1} + \beta_{t-1}$ $\beta_t = \beta_{t-1} + \zeta_{t}$ with ...
6
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1answer
923 views

Kalman filter vs. smoothing splines

Q: For which data is it appropriate to use state-space modeling and Kalman filtering instead of smoothing splines and vice versa? Is there some equivalence relationship between the two? I'm trying ...
13
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1answer
384 views

How to check which model is better in state space time series analysis?

I am doing time series data analysis by state space methods. With my data the stochastic local level model totally outperformed the deterministic one. But the deterministic level and slope model gives ...