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

## Author Info

• Michel Fliess

()

(LIX - Laboratoire d'informatique de l'école polytechnique - CNRS : UMR7161 - Polytechnique - X, INRIA Saclay - Ile de France - ALIEN - INRIA - Polytechnique - X - Ecole Centrale de Lille - CNRS : UMR8146)

• Cédric Join

()

(INRIA Saclay - Ile de France - ALIEN - INRIA - Polytechnique - X - Ecole Centrale de Lille - CNRS : UMR8146, CRAN - Centre de recherche en automatique de Nancy - CNRS : UMR7039 - Université Henri Poincaré - Nancy I - Institut National Polytechnique de Lorraine (INPL))

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## 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.

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File URL: http://hal.archives-ouvertes.fr/docs/00/33/90/65/PDF/Coventry-Finance.pdf

## Bibliographic Info

Paper provided by HAL in its series Post-Print with number inria-00338099.

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 Length: Date of creation: 2008 Date of revision: Publication status: Published - Presented, IAR-ACD08 (23rd IAR Workshop on Advanced Control and Diagnosis), 2008, Coventry, United Kingdom Handle: RePEc:hal:journl:inria-00338099 Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/inria-00338099/en/ Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

## References

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1. Andrew W. Lo & Harry Mamaysky & Jiang Wang, 2000. "Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation," NBER Working Papers 7613, National Bureau of Economic Research, Inc.
2. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-54, November.
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.
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