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I was intending to develop a paper work using Kalman Filter, but I have a few questions about this subject:

  1. What are the main differences between a simple AR Model and Kalman Filter? Would it be at the state equation? Because at the observation equation, we do the same kind of parameter estimation, don't we? If I was not right, what is the Kalman Filter benefit for parameter estimation?

  2. And between Dynamic Regression and Kalman Filter?

  3. What are the main advantages and disadvantages from Kalman Filter?

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    $\begingroup$ An autoregressive (AR) model is a time series model and the Kalman filter is an algorithm with several applications. They are not the same kind of tool or method, I don't see a straightforward way to compare them. What is the Kalman Filter benefit for parameter estimation? When an AR model is written in state-space form, the Kalman filter can be employed to evaluate the likelihood function. Thus, although it wans't its primary application, the Kalman filter turns out to be a convenient tool to obtain parameter estimates by maximum likelihood, as has been pointed in the answer by F. Tusell. $\endgroup$ – javlacalle Feb 12 '15 at 16:27
  • $\begingroup$ You are right, I understood that Kalman Filter is an algorithm, but I was thinking about State Space Models (Kalman Filter algorithm) and AR Model. AR Model parameter estimation is based on the total data amount for all period, isn't it? And the State Space/Kalman Filter is based only at the last observation, isn't it? $\endgroup$ – José Gomez Feb 12 '15 at 17:11
  • $\begingroup$ Your comment is not clear to me. It seems you are comparing two methods to estimate the parameters of an AR model, what methods are those? $\endgroup$ – javlacalle Feb 12 '15 at 18:23
  • $\begingroup$ My final objective is that I have a set of observations. At recent moments, two/three years before, these observations are varying over a huge range. And I need to forecast next periods. Nowadays, I am using VAR/VEC or ARIMA Models, but I was learning about State Space Forms and Kalman Filter that could help me to forecast better. I would like to understand better about Kalman Filter and explain what are the differences between SS Form/Kalman Filter estimation and others. After this, I wanna try to forecast using Kalman Filter algorithm and compare with my models. Thanks for your support. $\endgroup$ – José Gomez Feb 12 '15 at 19:27
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    $\begingroup$ Your question is too broad. The Kalman filter is not by itself a forecasting tool. The filter operates on an underlying model. In principle, the Kalman filter can be applied with any Gaussian linear model defined in a state-space form. This includes a wide range of models, ARIMA models, structural time series models, dynamic regression models,... Saying that you want to use the Kalman filter to obtain forecasts is a very broad statement and makes it difficult to give you any further feedback. $\endgroup$ – javlacalle Feb 12 '15 at 21:35
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You can cast and AR model in state-space form (and an ARMA model, or dynamic regression model). The Kalman filter is an algorithm that enables you to recursively compute the state vector (and the likelihood, with normal data): thus, it indirectly provides a way to maximize the likelihood.

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  • $\begingroup$ +1. In fact, R's arima function uses a state-space model under the hood. Poke into the data structure returned by arima and you'll see it. $\endgroup$ – Wayne Feb 12 '15 at 18:48

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