Characteristic times in stock market indices

L. Kullmann; J. Töyli; J. Kertesz; A. Kanto; K. Kaski

doi:10.1016/S0378-4371(99)00084-9

Characteristic times in stock market indices

L. Kullmann, J. Töyli, J. Kertesz, A. Kanto, K. Kaski

Research output: Contribution to journal › Conference article › peer-review

Abstract (may include machine translation)

In this study we analyze the Standard and Poor's 500 index data of the New York Stock Exchange for more than 32 years. Using a simple random walk model we demonstrate that the proper variable to look at is the logarithmic return. In the statistical analysis we have done fittings to the Levy distribution using either the index data as such or pre-processing it with ARCH, GARCH or IGARCH methods, which tend to remove the time-dependent variance. For short times the truncated Levy distribution is found to fit the data quite well. Since this is not a stable distribution, the scaling behavior observed for short times should brake down for longer times. We demonstrate that the characteristic time where this cross-over starts is of the order of one day.

Original language	English
Pages (from-to)	98-110
Number of pages	13
Journal	Physica A: Statistical Mechanics and its Applications
Volume	269
Issue number	1
DOIs	https://doi.org/10.1016/S0378-4371(99)00084-9
State	Published - 1 Jul 1999
Externally published	Yes
Event	Proceedings of the 1998 International Workshop on Econophysics and Statistical Finance - Palermo, Italy Duration: 28 Sep 1998 → 30 Sep 1998

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10.1016/S0378-4371(99)00084-9

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title = "Characteristic times in stock market indices",

abstract = "In this study we analyze the Standard and Poor's 500 index data of the New York Stock Exchange for more than 32 years. Using a simple random walk model we demonstrate that the proper variable to look at is the logarithmic return. In the statistical analysis we have done fittings to the Levy distribution using either the index data as such or pre-processing it with ARCH, GARCH or IGARCH methods, which tend to remove the time-dependent variance. For short times the truncated Levy distribution is found to fit the data quite well. Since this is not a stable distribution, the scaling behavior observed for short times should brake down for longer times. We demonstrate that the characteristic time where this cross-over starts is of the order of one day.",

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T1 - Characteristic times in stock market indices

AU - Kullmann, L.

AU - Töyli, J.

AU - Kertesz, J.

AU - Kanto, A.

AU - Kaski, K.

PY - 1999/7/1

Y1 - 1999/7/1

N2 - In this study we analyze the Standard and Poor's 500 index data of the New York Stock Exchange for more than 32 years. Using a simple random walk model we demonstrate that the proper variable to look at is the logarithmic return. In the statistical analysis we have done fittings to the Levy distribution using either the index data as such or pre-processing it with ARCH, GARCH or IGARCH methods, which tend to remove the time-dependent variance. For short times the truncated Levy distribution is found to fit the data quite well. Since this is not a stable distribution, the scaling behavior observed for short times should brake down for longer times. We demonstrate that the characteristic time where this cross-over starts is of the order of one day.

AB - In this study we analyze the Standard and Poor's 500 index data of the New York Stock Exchange for more than 32 years. Using a simple random walk model we demonstrate that the proper variable to look at is the logarithmic return. In the statistical analysis we have done fittings to the Levy distribution using either the index data as such or pre-processing it with ARCH, GARCH or IGARCH methods, which tend to remove the time-dependent variance. For short times the truncated Levy distribution is found to fit the data quite well. Since this is not a stable distribution, the scaling behavior observed for short times should brake down for longer times. We demonstrate that the characteristic time where this cross-over starts is of the order of one day.

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JO - Physica A: Statistical Mechanics and its Applications

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T2 - Proceedings of the 1998 International Workshop on Econophysics and Statistical Finance

Y2 - 28 September 1998 through 30 September 1998

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Characteristic times in stock market indices

Abstract (may include machine translation)

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