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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 ${\displaystyle \delta }$.

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 ${\displaystyle \delta }$. 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 ${\displaystyle \delta }$.

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 ${\displaystyle N(\delta )}$ observed over the fixed period to the size of the threshold ${\displaystyle \delta }$:

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

where ${\displaystyle C_{N,DC}}$ and ${\displaystyle E_{N,DC}}$ 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.

• 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.