# Fractal structure of financial high frequency data

9 引用 (Scopus)

### 抄録

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.

元の言語 English 13-18 6 Fractals 10 1 https://doi.org/10.1142/S0218348X02001002 Published - 2002 Yes

### Fingerprint

High-frequency Data
Fractal Structure
Financial Data
Fractals
Extreme Values
Transaction Costs
Fractal dimension
Scaling Behavior
Fractal Dimension
Time series
Time-varying
Interpolation
Time Scales
Fold
Interpolate
Sampling
Interval
Costs

### ASJC Scopus subject areas

• General
• Geometry and Topology

### これを引用

：: Fractals, 巻 10, 番号 1, 2002, p. 13-18.

title = "Fractal structure of financial high frequency data",
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.",
author = "Yoshiaki Kumagai",
year = "2002",
doi = "10.1142/S0218348X02001002",
language = "English",
volume = "10",
pages = "13--18",
journal = "Fractals",
issn = "0218-348X",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "1",

}

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.

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U2 - 10.1142/S0218348X02001002

DO - 10.1142/S0218348X02001002

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JO - Fractals

JF - Fractals

SN - 0218-348X

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ER -