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

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20 views

Difference between particle filter (PF) and recurrent neural network (RNN) for time series

Both method are used to estimate time series from data. The question is, when should I use one method or other? Is any advantage to use one instead of the other? I know that in a PF there is a hidden ...
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18 views

Predicting a Chi-Square Process

Assume that $W(t)$ is a one-parameter stochastic process given by $W(t) := X_1^2(t) + X_2^2(t)$ where $X_i(t)$ are independent copies of a stationary gaussian process with known covariance function. ...
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17 views

State space modelling of longitudinal data in r

I have n stations, and for each station there are m time series observations on different days, each of length ...
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1answer
37 views

Intuitive explanation of state space models

Having looked into options for modelling and forecasting a financial time series based on mixed frequency data, I came across state space models, which seems worth exploring. I've however been ...
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44 views

Maximum Likelihood estimation and the Kalman filter

I know the Kalman filter recursions and can derive these but what I don't really get is how to estimate the hyper parameters using maximum likelihood. I understand that when running the Kalman filter ...
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1answer
73 views

State space model estimation

I would like to estimate this system with state space modeling in order to perform some initial tests as an empirical analysis. $ \begin{cases} x_t = \mu_t + \beta_1x_t + \varepsilon \\ \mu_t = c_{t-...
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1answer
39 views

Estimation of the local trend models (State Space) through ML

Tsay, R. S. (2010), Analysis of Financial Time Series, 2nd Edition, discusses on page 504 the estimation of local trend models (state space). The measurement and the transition equations are as ...
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1answer
37 views

How to do predictions using a state-space model

I am completely new to HMM's and state space models, so I have a very naive question. I have a classic state space model: x_t = Ax_{t-1} + w_t y_t = Cx_t + v_t ...
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19 views

K-fold cross validation error in CausalImpact

I want to know how to get the prediction error in CausalImpact()function of CausalImpact R package. I am looking for something like 10 fold cross validation error?
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21 views

model choice multi state sequence prediction (and possible R packages for solving problem)

I have a set of sequences (dataset) where I have sequences of letters. I also have a corresponding response sequences where the known state of the sequence are. I would very much like to make a ...
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1answer
80 views

Are particle filters necessarily linked to state-space models?

I have been asked to look into using particle filters on financial time series. All the sources I have found describe particles filters in the context of state-space models. Are particle filters and ...
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38 views

Non-Gaussian state-space models

I am curious why most literature mentions that only gaussian state-space models (such as kalman) are analytically tractable. I was curious about posterior inference on a Gamma chain, why would it be ...
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29 views

Formulation of State Space Models

I have seen the following formulation of state space models: $$ z_{t + 1} = A z_t + B u_t + \epsilon_t \\ y_t = C z_t + D u_t + \delta_t $$ But sometimes it is also written as follows: $$ z_{t} = ...
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44 views

State space model affected from future events?

I understand that a state-space model is a common model where the current observation $y_t$ depends on the current state $x_t$. Is there any common model where the current observation $y_t$ depends ...
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18 views

State-space models for specifying rare events

I wonder if state-space models in the sense of Durbin and Koopman's book can be employed to represent time series in which a considerable amount of time the value is zero, followed by an abrupt change ...
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236 views

Switch from Modelling a Process using a Poisson Distribution to use a Negative Binomial Distribution?

We have a random process that may-or-may-not occur multiple times in a set period of time $T$. We have a data feed from a pre-existing model of this process, that provides the probability of a number ...
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1answer
38 views

Noise identification in Kalman filtering procedure

Suppose I have a standard state-space model. The sample is, say, 1990-2015, quarterly data. I assume that in period 1990-2000 there were two sources of noise in the measurement equation, while in 2001-...
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60 views

State Space Model Specification (KFAS)

I am using KFAS to fit a dynamic logistic model of the form; $\hat{y} = \bf \beta_t x + \epsilon$ $\beta_t = \beta_{t-1} + \eta$ So the regression parameters change over time, and act as latent ...
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1answer
53 views

Missing Data in CausalImpact and Additional Covariates

I am looking at the fantastic R package CausalImpact and had a couple questions hopefully someone can help with. What should be done when there are 0 values in a ...
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1answer
54 views

writing down likelihood for dynamic state space model?

I have a discrete-time state space model where observations depend on a latent rate $X$. The prior on the rate is $X \sim \mathrm{Normal}(\mu_x, \sigma_x)$. Each observation $Y_t$ is generated using ...
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48 views

SSM with a regression component with R (dlm)

I am trying to fit the following state space model. (1) Kt = K(t-1)* + ε1t (2) Yt = Kt + βZt + ε2t where, t is time, Yt is the observable variable (at t), Kt is the unobservable trend, and Zt is a ...
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2answers
54 views

How to show that any Gaussian time-series is linear one?

In this paper I saw the following statement: If the time series is Gaussian (i.e., normally distributed) then the best linear forecast is in fact the best of all possible forecasts: No ...
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35 views

What nonlinear extension of ARMA and State Space Model do exist?

In ARMA model we postulate that predictions of time series can be calculated as a linear function of $N$ previous observations (AR part) and $K$ differences between the previous observations and the ...
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1answer
81 views

What are the more Advanced models for time series

As far as my studies go, I did: ARIMA in all sauces Dynamic linear models/state space model. The basics VAR(IMA) VECM I then tried to see if there is a model that combines some or most of the ...
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108 views

ARIMA(1,1,1) model to state space form

It's easy for me to fit ARIMA models in software such as R but I cannot find a "simple" example anywhere on the web for how to transform an ARIMA model to state space form (SSF)? I think it's the ...
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9 views

ML estimation - properties of mixed stationary non-stationary process

i try to estimate the following state space model: Measurement equation y(t) = a(t) + b(t) Transition equations a(t) = a(t-1) + e(t) b(t) = C*b(t-1) + u(t) where the observations y(t) are ...
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1answer
141 views

Find state space model to compare with Box-Jenkins ARIMA model

I asked a question here about how to get predictions for the random-walk component of an ARIMA model. Are there time series models in the state-space framework that might be suitable for the kind of ...
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18 views

Categorical distribution with time dependent parameters

I have a time series of categorical data: On any given day $t$ a vector $\vec{x}_t$ is observed of length $K=200$ where one element is $1$ and the rest are $0$. I have reason to believe that the ...
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1answer
179 views

Assumptions in CausalImpact package

I'm using the R package CausalImpact (Brodersen et. al, 2015) to estimate the impact of and event in a time series of tourists arrivals in a country. I compare it with other series of other countries ...
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1answer
41 views

JAGS, RJAGS: simple way to track the moment of a chain instead of the entire chain?

I have a state-space model coded into JAGS. The model predicts the latent state at each observation with ~40,000 observations. In rJAGS I can store the chains of the latent state, '$z$', but having a ...
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27 views

Statistical significance of state space models

I built a state-space model of time-series data and I want to examine the significance of estimated model parameters. Is there any method to address this issue? What statistical test should be used?
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1answer
57 views

How to report simple markov transition matrix

I have a beginners question on Markov chains. We found that a Markov chain might be a good way to describe the data we got from our experiment. Let's say we have two simple Markov transition matrix ...
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37 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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75 views

Estimating Kalman Filter parameters from repeated measurement of a process with 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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27 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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17 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
64 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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33 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. ...
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170 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
324 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 python-...
2
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1answer
123 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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48 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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2answers
364 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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154 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 h-...
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111 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
29 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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145 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 ...
3
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308 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
80 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
86 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 ...