View source for 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 <math>\delta</math>. 
[[File:Directional-change dissection procedure.png|thumb|'''Figure 1:''' A financial market price curve (grey) dissected by a set of directional-changes (grey squares). The size of the threshold of the operator is shown in the middle of the figure. Local extremes are marked by grey circles. The timeline contains intervals of equal length in physical time and the length of the intervals based on the  directional-change operator.]]
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.<ref>{{Cite journal|last1=Guillaume|first1=Dominique M.|last2=Dacorogna|first2=Michel M.|last3=Davé|first3=Rakhal R.|last4=Müller|first4=Ulrich A.|last5=Olsen|first5=Richard B.|last6=Pictet|first6=Olivier V.|date=1997-04-01|title=From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets|journal=Finance and Stochastics|language=en|volume=1|issue=2|pages=95–129|doi=10.1007/s007800050018|issn=0949-2984|doi-access=free}}</ref> 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 (signal)|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 (finance)|volatility]] of price changes conditional to (2) the selected threshold <math>\delta</math>. The [[Stochastic process|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 reduction|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 <math>\delta</math>. 

== Application ==
The directional-change intrinsic time operator was used to analyze high frequency [[Foreign exchange market|foreign exchange]] market data and has led to the discovery of a large set of [[Power law|scaling laws]] that have not been previously observed.<ref>{{Cite journal|last1=Glattfelder|first1=J. B.|last2=Dupuis|first2=A.|last3=Olsen|first3=R. B.|date=2011-04-01|title=Patterns in high-frequency FX data: discovery of 12 empirical scaling laws|journal=Quantitative Finance|volume=11|issue=4|pages=599–614|doi=10.1080/14697688.2010.481632|arxiv=0809.1040|s2cid=154979612|issn=1469-7688}}</ref> 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 <math>N(\delta)</math> observed over the fixed period to the size of the threshold <math>\delta</math>:

<math>N(\delta) = \left( \frac{\delta}{C_{N, DC}} \right)^{E_{N, DC}}</math>,

where <math>C_{N, DC}</math> and <math>E_{N, DC}</math> are the [[Power law|scaling law]] coefficients.<ref>{{Cite journal|last1=Guillaume|first1=Dominique M.|last2=Dacorogna|first2=Michel M.|last3=Davé|first3=Rakhal R.|last4=Müller|first4=Ulrich A.|last5=Olsen|first5=Richard B.|last6=Pictet|first6=Olivier V.|date=1997-04-01|title=From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets|journal=Finance and Stochastics|language=en|volume=1|issue=2|pages=95–129|doi=10.1007/s007800050018|issn=0949-2984|doi-access=free}}</ref>

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

* trading strategy characterised by the annual [[Sharpe ratio]] 3.04<ref>{{cite book
 | last1 = Golub | first1 = Anton
 | last2 = Glattfelder | first2 = James B.
 | last3 = Olsen | first3 = Richard B.
 | editor1-last = Dempster | editor1-first = M. A. H.
 | editor2-last = Kanniainen | editor2-first = Juho
 | editor3-last = Keane | editor3-first = John
 | editor4-last = Vynckier | editor4-first = Erik
 | contribution = The Alpha Engine: Designing an Automated Trading Algorithm
 | date = February 2018
 | doi = 10.1201/9781315372006-3
 | isbn = 9781315372006
 | pages = 49–76
 | publisher = Chapman and Hall/CRC
 | ssrn = 2951348
 | title = High-Performance Computing in Finance}}</ref>
* tools designed to monitor [[Market liquidity|liquidity]] at multiple trend scales.<ref>{{Cite journal|last1=Golub|first1=Anton|last2=Chliamovitch|first2=Gregor|last3=Dupuis|first3=Alexandre|last4=Chopard|first4=Bastien|date=2016-01-01|title=Multi-scale representation of high frequency market liquidity|journal=Algorithmic Finance|language=en|volume=5|issue=1–2|pages=3–19|doi=10.3233/AF-160054|issn=2158-5571|doi-access=free|arxiv=1402.2198}}</ref>

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 [[Big data|BigData]].

== References ==
* [[File:CC-BY icon.svg|50px]]  Text in this draft was copied from {{cite journal |last1=Petrov |first1=Vladimir |last2=Golub |first2=Anton |last3=Olsen |first3=Richard |title=Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time |journal=Journal of Risk and Financial Management |date=2019 |volume=12 |issue=2 |pages=54 |doi=10.3390/jrfm12020054 |language=en|doi-access=free |hdl=10419/239003 |hdl-access=free }}, which is available under a [https://creativecommons.org/licenses/by/4.0/  Creative Commons Attribution 4.0 International License].
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[[Category:Data analysis]]