A martingale decomposition of discrete Markov chains
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1873-7374; 0165-1765
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Economics letters, 2015, Vol. 133, pp. 14-18
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HANSEN, Peter Reinhard, A martingale decomposition of discrete Markov chains, Economics letters, 2015, Vol. 133, pp. 14-18 - https://hdl.handle.net/1814/38564
Abstract
We consider a multivariate time series whose increments are given from a homogeneous Markov chain. We show that the martingale component of this process can be extracted by a filtering method and establish the corresponding martingale decomposition in closed-form. This representation is useful for the analysis of time series that are confined to a grid, such as financial high frequency data.
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Available online 30 April 2015.