Estimating models based on Markov jump processes given fragmented observation series |
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Authors: | Markus Hahn Sylvia Frühwirth-Schnatter Jörn Sass |
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Institution: | (1) Department of Information Sciences, Tokyo University of Sciences, Chiba 278-8510, Japan |
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Abstract: | We consider the problem of estimating the rate matrix governing a finite-state Markov jump process given a number of fragmented
time series. We propose to concatenate the observed series and to employ the emerging non-Markov process for estimation. We
describe the bias arising if standard methods for Markov processes are used for the concatenated process, and provide a post-processing
method to correct for this bias. This method applies to discrete-time Markov chains and to more general models based on Markov
jump processes where the underlying state process is not observed directly. This is demonstrated in detail for a Markov switching
model. We provide applications to simulated time series and to financial market data, where estimators resulting from maximum
likelihood methods and Markov chain Monte Carlo sampling are improved using the presented correction. |
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