A symmetry-guided time redefinition may enhance and simplify analyses of historical series displaying recurrent patterns . Enforcing a simple-scaling symmetry with Hurst exponent 1/2 and the requirement of increments' stationarity , we identify a time-definition protocol in the financial case. The novel time scale, constructed through a systematic application of the Kolmogorov-Smirnov criterion to extensive data of the S P500 index, lays a bridge between the regime of minutes and that of several days in physical time. It allows us to quantify the duration of periods in which the market is inactive , like amid nights, and to optimally exploit the statistical information contained in the series.The overall strategy leads to a significant reduction of multiscaling features, once the moments of the return probability density function are analyzed versus the novel time .
A symmetry-guided definition of time may enhance and simplify the analysis of historical series with recurrent patterns and seasonalities. By enforcing simple-scaling and stationarity of the distributions of returns , we identify a successful protocol of time definition in Finance. The essential structure of the stochastic process underlying the series can thus be analyzed within a most parsimonious symmetry scheme in which multiscaling is reduced in the quest of a time scale additive and independent of moment-order in the distribution of returns. At the same time, duration of periods in which markets remain inactive are properly quantified by the novel clock, and the corresponding (e.g., overnight) returns are consistently taken into account for financial applications .
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time redefinition
definition of time
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analyses
the analysis
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displaying recurrent patterns . Enforcing a
with recurrent patterns and seasonalities. By enforcing
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symmetry with Hurst exponent 1/2 and the requirement of increments' stationarity
and stationarity of the distributions of returns
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time-definition protocol in the financial case. The novel time scale, constructed through a systematic application of the Kolmogorov-Smirnov criterion to extensive data of the S
R
P500 index, lays a bridge between the regime of minutes and that of several days in physical time. It allows us to quantify the
successful protocol of time definition in Finance. The essential structure of the stochastic process underlying the series can thus be analyzed within a most parsimonious symmetry scheme in which multiscaling is reduced in the quest of a time scale additive and independent of moment-order in the distribution of returns. At the same time,
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the market is inactive , like amid nights, and to optimally exploit the statistical information contained in the series.The overall strategy leads to a significant reduction of multiscaling features, once the moments of the return probability density function are analyzed versus the novel time
markets remain inactive are properly quantified by the novel clock, and the corresponding (e.g., overnight) returns are consistently taken into account for financial applications