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Time Series Technical Analysis via New Fast Estimation Methods: A Preliminary Study in Mathematical Finance

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  • Michel Fliess

    (LIX, INRIA Saclay - Ile de France)

  • C'edric Join

    (INRIA Saclay - Ile de France, CRAN)

Abstract

New fast estimation methods stemming from control theory lead to a fresh look at time series, which bears some resemblance to "technical analysis". The results are applied to a typical object of financial engineering, namely the forecast of foreign exchange rates, via a "model-free" setting, i.e., via repeated identifications of low order linear difference equations on sliding short time windows. Several convincing computer simulations, including the prediction of the position and of the volatility with respect to the forecasted trendline, are provided. $\mathcal{Z}$-transform and differential algebra are the main mathematical tools.

Suggested Citation

  • Michel Fliess & C'edric Join, 2008. "Time Series Technical Analysis via New Fast Estimation Methods: A Preliminary Study in Mathematical Finance," Papers 0811.1561, arXiv.org, revised Nov 2008.
    • Handle: RePEc:arx:papers:0811.1561
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    References listed on IDEAS

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    1. repec:bla:jfinan:v:55:y:2000:i:4:p:1705-1770 is not listed on IDEAS
    2. Andrew W. Lo & Harry Mamaysky & Jiang Wang, 2000. "Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation," Journal of Finance, American Finance Association, vol. 55(4), pages 1705-1765, August.
    3. Michel Fliess & C'edric Join, 2009. "A mathematical proof of the existence of trends in financial time series," Papers 0901.1945, arXiv.org.
    4. Michel Fliess & Cédric Join, 2009. "A mathematical proof of the existence of trends in financial time series," Post-Print inria-00352834, HAL.
    5. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
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