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A Martingale Decomposition of Discrete Markov Chains

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  • Peter Reinhard Hansen

    (European University Institute and CREATES)

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.

Suggested Citation

  • Peter Reinhard Hansen, 2015. "A Martingale Decomposition of Discrete Markov Chains," CREATES Research Papers 2015-18, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2015-18
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    References listed on IDEAS

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    7. Peter Reinhard Hansen & Guillaume Horel, 2009. "Quadratic Variation by Markov Chains," CREATES Research Papers 2009-13, Department of Economics and Business Economics, Aarhus University.
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    Cited by:

    1. Peter Reinhard Hansen & Yiyao Luo, 2023. "Robust Estimation of Realized Correlation: New Insight about Intraday Fluctuations in Market Betas," Papers 2310.19992, arXiv.org.
    2. Bian, Siyu & Serra, Teresa & Garcia, Philip & Irwin, Scott, 2022. "New evidence on market response to public announcements in the presence of microstructure noise," European Journal of Operational Research, Elsevier, vol. 298(2), pages 785-800.

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    More about this item

    Keywords

    Markov Chain; Martingale; Beveridge-Nelson Decomposition;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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