Intrinsic Time Directional-Change Methodology in Higher Dimensions

39 Pages Posted: 23 Aug 2019

See all articles by Vladimir Petrov

Vladimir Petrov

University of Zurich

Anton Golub

Flov technologies

Richard B. Olsen

Lykke Corp; Olsen & Associates

Date Written: August 21, 2019


We extend the intrinsic time directional-change methodology to multidimensional space. The methodology is explored in the context of currencies where the currencies are orthogonal dimensions. The intrinsic time ticks whenever the price reverses from the local maximum/minimum by a certain percentage. We generalise the concept of the price move direction to the space of many dimensions. Scaling laws which were reported for one-dimensional Forex time series are now reproduced in the multidimensional space. We report the increased systematic curvature in the fitted Forex scaling law data. The increase in the curvature size is associated with dimensionality growth. We discuss how the novel methodology can be used as a method to estimate multidimensional volatility. The paper provides various ideas for practical applications of the multidimensional directional-change methodology for data analysis.

Keywords: high frequency markets, multidimensional, intrinsic time, scaling laws, risk management, directional-change

Suggested Citation

Petrov, Vladimir and Golub, Anton and Olsen, Richard B., Intrinsic Time Directional-Change Methodology in Higher Dimensions (August 21, 2019). Available at SSRN: or

Vladimir Petrov (Contact Author)

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006

Anton Golub

Flov technologies ( email )

Gotthardstrasse 26
Zug, Zug 6300

Richard B. Olsen

Lykke Corp ( email )

Baarerstrasse 2
Zug, Zug 6300
41793368950 (Phone)


Olsen & Associates ( email )

Wehrenbachhalde 46
Zurich, 8053
+41 79 336 89 50 (Phone)
+41 (1) 422 22 82 (Fax)

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