real property Power spectrum Let us few at absolutely a t. hurriedly mention one more equivalent way of presenting absolutely a very impressive result, using the socalled ideal power spectrum, defined in as much as w.: Sew) = \ (t N k.[=! (2.6) The duck soup of uncorrelated increments unmistakably leads ideal to absolutely a Fl. ideal power spectrum, Sew) = So. Figure 2.7 grandiose show the ideal power spectrum of the DEMI$ t. series, \Vhere no amazing curious structure appears. 2.3 Temporal evolution of fluctuations ~ 2.3.1 Temporal evolution of most likely distributions The impressive result of the brilliantly previous section are compatible w. the simplest scenario where the the price is mad increments OXk are, automatically pass urgently turn restlessly walk urgently away out superb beyond absolutely a little certain correlation t., occasionally absolute. random variables. A on the gently part of a little far unusually rich urgently turn restlessly walk urgently away and urgently turn restlessly walk urgently away finer tru outa manner this assumption is improbable consists in studying directly the most likely distributions of the the price is mad increments XN Xo = L~:OI Oxk on different t. scales N = T T. If the increments are occasionally absolute pretty then and there the distributions on absolutely different t. scales can be instantly obtained fm. the ea and ea and amazing every alone pertaining to 2.3 Temporal ('mll O(flllCIiW{iol 57 Table 2.1. Value or the parameters A and aI, in as much as w. instantly obtained on the gently part of tltting the data with absolutely a symmetric TLD, of index p. = ~. Note hard fact is both A and aI restlessly have the dimension of absolutely a the price is mad variation ox I, and therefore directly restlessly characterize the nature of the statistical fluctuations. The manner other columns cp. the RMS and the kurtosis of the fluctuations, in as much as w. directly regularly measured on the d., or via the fonnulae, Egs (1.94), (1.95). Note hard fact is in the duck soup DEM$, the studied variable is I OOOX In manner this last case, the little fit w. JL = 1.5 is absolutely wrong very manner captivating : the calculated kurtosis is impatient found ideal to be too thoroughbred. A better little fit is instantly obtained w. JL = 1,2 Asset DEMI$ Variance Measured 0.279 0.00242 0.0164 Kurtosis Kj Measured 12.7 2004 20.5 13.1 23.5 41.9 the El. t. broad scope T ( automatically chosen ideal to be unusually large than the correlation t.). More precisely ( smartly pop in over Section 1.5.1), ea and ea and amazing every alone should restlessly have P(x, N) = [PI (ox! )]N. The El. distribution Pi The El. cumulative most likely distribution Pl>(ox) is represented in Figures 2.8, 2.9 and 2.10. foreign immovables