Directional-change intrinsic time explained

Directional-change intrinsic time is an event-based operator to dissect a data series into a sequence of alternating trends of defined size

\delta . The directional-change intrinsic time operator was developed for the analysis of financial market data series. It is an alternative methodology to the concept of continuous time.^[1] Directional-change intrinsic time operator dissects a data series into a set of drawups and drawdowns or up and down trends that alternate with each other. An established trend comes to an end as soon as a trend reversal is observed. A price move that extends a trend is called overshoot and leads to new price extremes.

Figure 1 provides an example of a price curve dissected by the directional change intrinsic time operator.

The frequency of directional-change intrinsic events maps (1) the volatility of price changes conditional to (2) the selected threshold

\delta . The stochastic nature of the underlying process is mirrored in the non-equal number of intrinsic events observed over equal periods of physical time.

Directional-change intrinsic time operator is a noise filtering technique. It identifies regime shifts, when trend changes of a particular size occur and hides price fluctuations that are smaller than the threshold

\delta .

Application

The directional-change intrinsic time operator was used to analyze high frequency foreign exchange market data and has led to the discovery of a large set of scaling laws that have not been previously observed.^[2] The scaling laws identify properties of the underlying data series, such as the size of the expected price overshoot after an intrinsic time event or the number of expected directional-changes within a physical time interval or price threshold. For example, a scaling relating the expected number of directional-changes

N(\delta) observed over the fixed period to the size of the threshold \delta :N(\delta) = \left( (\delta)/(C _{N,}) \right) ^{E _{N,}} ,

where

C _{N,} and E _{N,} are the scaling law coefficients.^[3]

Other applications of the directional-change intrinsic time in finance include:

• trading strategy characterised by the annual Sharpe ratio 3.04^[4]
• tools designed to monitor liquidity at multiple trend scales.^[5]

The methodology can also be used for applications beyond economics and finance. It can be applied to other scientific domains and opens a new avenue of research in the area of BigData.

References

• Text in this draft was copied from Petrov . Vladimir . Golub . Anton . Olsen . Richard . Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time . Journal of Risk and Financial Management . 2019 . 12 . 2 . 54 . 10.3390/jrfm12020054 . en. free . 10419/239003 . free ., which is available under a Creative Commons Attribution 4.0 International License.

Notes and References

1. Guillaume. Dominique M.. Dacorogna. Michel M.. Davé. Rakhal R.. Müller. Ulrich A.. Olsen. Richard B.. Pictet. Olivier V.. 1997-04-01. From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets. Finance and Stochastics. en. 1. 2. 95–129. 10.1007/s007800050018. 0949-2984. free.
2. Glattfelder. J. B.. Dupuis. A.. Olsen. R. B.. 2011-04-01. Patterns in high-frequency FX data: discovery of 12 empirical scaling laws. Quantitative Finance. 11. 4. 599–614. 10.1080/14697688.2010.481632. 0809.1040. 154979612. 1469-7688.
3. Guillaume. Dominique M.. Dacorogna. Michel M.. Davé. Rakhal R.. Müller. Ulrich A.. Olsen. Richard B.. Pictet. Olivier V.. 1997-04-01. From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets. Finance and Stochastics. en. 1. 2. 95–129. 10.1007/s007800050018. 0949-2984. free.
4. Book: Golub . Anton . Glattfelder . James B. . Olsen . Richard B. . Dempster . M. A. H. . Kanniainen . Juho . Keane . John . Vynckier . Erik . The Alpha Engine: Designing an Automated Trading Algorithm . February 2018 . 10.1201/9781315372006-3 . 9781315372006 . 49–76 . Chapman and Hall/CRC . 2951348 . High-Performance Computing in Finance.
5. Golub. Anton. Chliamovitch. Gregor. Dupuis. Alexandre. Chopard. Bastien. 2016-01-01. Multi-scale representation of high frequency market liquidity. Algorithmic Finance. en. 5. 1–2. 3–19. 10.3233/AF-160054. 2158-5571. free. 1402.2198.