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.
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