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A martingale decomposition of discrete Markov chains

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  • Hansen, Peter Reinhard

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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  • Hansen, Peter Reinhard, 2015. "A martingale decomposition of discrete Markov chains," Economics Letters, Elsevier, vol. 133(C), pages 14-18.
    • Handle: RePEc:eee:ecolet:v:133:y:2015:i:c:p:14-18
    DOI: 10.1016/j.econlet.2015.04.028
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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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