Directional-change intrinsic time

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 $\delta$ :

$N(\delta )=\left({\frac {\delta }{C_{N,DC}}}\right)^{E_{N,DC}}$ ,

where $C_{N,DC}$ and $E_{N,DC}$ 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 (2019). "Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time". Journal of Risk and Financial Management. 12 (2): 54. doi:10.3390/jrfm12020054. hdl:10419/239003., which is available under a Creative Commons Attribution 4.0 International License.

^ 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. 1 (2): 95–129. doi:10.1007/s007800050018. ISSN 0949-2984.
^ 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. arXiv:0809.1040. doi:10.1080/14697688.2010.481632. ISSN 1469-7688. S2CID 154979612.
^ 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. 1 (2): 95–129. doi:10.1007/s007800050018. ISSN 0949-2984.
^ Golub, Anton; Glattfelder, James B.; Olsen, Richard B. (February 2018). "The Alpha Engine: Designing an Automated Trading Algorithm". In Dempster, M. A. H.; Kanniainen, Juho; Keane, John; Vynckier, Erik (eds.). High-Performance Computing in Finance. Chapman and Hall/CRC. pp. 49–76. doi:10.1201/9781315372006-3. ISBN 9781315372006. SSRN 2951348.
^ Golub, Anton; Chliamovitch, Gregor; Dupuis, Alexandre; Chopard, Bastien (2016-01-01). "Multi-scale representation of high frequency market liquidity". Algorithmic Finance. 5 (1–2): 3–19. arXiv:1402.2198. doi:10.3233/AF-160054. ISSN 2158-5571.

[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. 1 (2): 95–129. doi:10.1007/s007800050018. ISSN 0949-2984.

[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. arXiv:0809.1040. doi:10.1080/14697688.2010.481632. ISSN 1469-7688. S2CID 154979612.

[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. 1 (2): 95–129. doi:10.1007/s007800050018. ISSN 0949-2984.

[4] Golub, Anton; Glattfelder, James B.; Olsen, Richard B. (February 2018). "The Alpha Engine: Designing an Automated Trading Algorithm". In Dempster, M. A. H.; Kanniainen, Juho; Keane, John; Vynckier, Erik (eds.). High-Performance Computing in Finance. Chapman and Hall/CRC. pp. 49–76. doi:10.1201/9781315372006-3. ISBN 9781315372006. SSRN 2951348.

[5] Golub, Anton; Chliamovitch, Gregor; Dupuis, Alexandre; Chopard, Bastien (2016-01-01). "Multi-scale representation of high frequency market liquidity". Algorithmic Finance. 5 (1–2): 3–19. arXiv:1402.2198. doi:10.3233/AF-160054. ISSN 2158-5571.

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