Abstract
We propose a new method to describe scaling behavior of time series. We introduce an extension of extreme values. Using these extreme values determined by a scale, we define some functions. Moreover, using these functions, we can measure a kind of fractal dimension - fold dimension. In financial high frequency data, observations can occur at varying time intervals. Using these functions, we can analyze non-equidistant data without interpolation or evenly sampling. Further, the problem of choosing the appropriate time scale is avoided. Lastly, these functions are related to a viewpoint of investor whose transaction costs coincide with the spread.
| Original language | English |
|---|---|
| Pages (from-to) | 13-18 |
| Number of pages | 6 |
| Journal | Fractals |
| Volume | 10 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2002 |
| Externally published | Yes |
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ASJC Scopus subject areas
- General
- Geometry and Topology
Cite this
Fractal structure of financial high frequency data. / Kumagai, Yoshiaki.
In: Fractals, Vol. 10, No. 1, 2002, p. 13-18.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Fractal structure of financial high frequency data
AU - Kumagai, Yoshiaki
PY - 2002
Y1 - 2002
N2 - We propose a new method to describe scaling behavior of time series. We introduce an extension of extreme values. Using these extreme values determined by a scale, we define some functions. Moreover, using these functions, we can measure a kind of fractal dimension - fold dimension. In financial high frequency data, observations can occur at varying time intervals. Using these functions, we can analyze non-equidistant data without interpolation or evenly sampling. Further, the problem of choosing the appropriate time scale is avoided. Lastly, these functions are related to a viewpoint of investor whose transaction costs coincide with the spread.
AB - We propose a new method to describe scaling behavior of time series. We introduce an extension of extreme values. Using these extreme values determined by a scale, we define some functions. Moreover, using these functions, we can measure a kind of fractal dimension - fold dimension. In financial high frequency data, observations can occur at varying time intervals. Using these functions, we can analyze non-equidistant data without interpolation or evenly sampling. Further, the problem of choosing the appropriate time scale is avoided. Lastly, these functions are related to a viewpoint of investor whose transaction costs coincide with the spread.
UR - http://www.scopus.com/inward/record.url?scp=0036337797&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036337797&partnerID=8YFLogxK
U2 - 10.1142/S0218348X02001002
DO - 10.1142/S0218348X02001002
M3 - Article
AN - SCOPUS:0036337797
VL - 10
SP - 13
EP - 18
JO - Fractals
JF - Fractals
SN - 0218-348X
IS - 1
ER -