Comparison between volatility return intervals of the S&;P 500
index and two common models |
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Authors: | I Vodenska-Chitkushev F Z Wang P Weber K Yamasaki S Havlin H E Stanley |
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Institution: | 1.Center for Polymer Studies and Department of Physics,Boston University,Boston,USA;2.Institute for Theoretical Physics, University of Cologne,K?ln,Germany;3.Department of Environmental Sciences,Tokyo University of Information Sciences,Chiba,Japan;4.Minerva Center and Department of Physics,Bar-Ilan University,Ramat-Gan,Israel |
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Abstract: | We analyze the S&P 500 index data for the 13-year period, from
January 1, 1984 to December 31, 1996, with one data point every 10
min. For this database, we study the distribution and clustering
of volatility return intervals, which are defined as the time
intervals between successive volatilities above a certain threshold
q. We find that the long memory in the volatility leads to a
clustering of above-median as well as below-median return intervals.
In addition, it turns out that the short return intervals form
larger clusters compared to the long return intervals. When
comparing the empirical results to the ARMA-FIGARCH and fBm models
for volatility, we find that the fBm model predicts scaling better
than the ARMA-FIGARCH model, which is consistent with the argument
that both ARMA-FIGARCH and fBm capture the long-term dependence in
return intervals to a certain extent, but only fBm accounts for the
scaling. We perform the Student's t-test to compare the empirical
data with the shuffled records, ARMA-FIGARCH and fBm. We analyze
separately the clusters of above-median return intervals and the
clusters of below-median return intervals for different thresholds
q. We find that the empirical data are statistically different
from the shuffled data for all thresholds q. Our results also
suggest that the ARMA-FIGARCH model is statistically different from
the S&P 500 for intermediate q for both above-median and
below-median clusters, while fBm is statistically different from
S&P 500 for small and large q for above-median clusters and for
small q for below-median clusters. Neither model can fully explain
the entire regime of q studied. |
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Keywords: | 89 65 Gh Economics econophysics financial markets business and management 05 45 Tp Time series analysis 89 75 Da Systems obeying scaling laws |
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