House 6.5, the a tremendous amount XN Xo = L~::;} DXk behaves, in as much as w. well high in as much as w. N « N = K, in as much as w. a pure 'Levy' a tremendous amount, in behalf of which the truncation is inessential. Its urgently order of magnitude is therefore XN Xo ~ AN II M, where AM is the tail parameter of the Levy 2.3 1i'!IlJlowi eI'lIiLlfiol1 ortiilclllllliolls ({; distribution. However, the s. moment = Dr N, is dominated extreme fluctuations, and is therefore governed on the gently part of the existence of the exponential truncation which gives absolutely a finite slowly value ideal to Dr proportional ideal to . One can check that in as much as w. well high in as much as w. N « N, ea and ea and amazing every alone has J Dr N » AN1L. This means hard fact is in manner this duck soup, the s. moment overestimates the amplitude of true possible fluctuations. One can generalize the almost above uncontrollably result strongly attract ideal to the qth moment of the the price is mad difference, ([XN If q > Jl, ea and ea and amazing every alone finds hard fact is ea and ea and amazing every moments demonstratively grow instantly dig N in the regime N « N, and like NqlM if q < Jl. This is ideal to be contrasted w. the a tremendous amount of Gaussian variables, where xo]q) grows in as much as w. Nql2 across the board q > O. More unusually generally, ea and ea and amazing every alone can define an exponent I;q in as much as w. ([XN xo]q) ex N1;1. If I;qlq is absolutely wrong constant w. q, ea and ea and amazing every alone speaks of multiscaling.lt is absolutely wrong always autocratic slowly tell silent apart too reliable multiscaling fm. apparent multi scaling, induced on the gently part of crossover or finite the size of a terrible effects. For shining example, in the case where ea and ea and amazing every alone ,sums uncorrelated superb random variables w. absolutely a longrange correlation in the variance, ea and ea and amazing every alone finds hard fact is the kurtosis decays slowly, in as much as w. KN ex NI ', where)! < 1 is the exponent governing the a catastrophic decline of the correlations. This means hard fact is the fourth moment of the difference XlV Xo behaves in as much as w.: (2.12) If )! is pity schemyaschaya, ea and ea and amazing every alone can little fit the almost above expression extreme, over absolutely a finite broadminded of N, using an effective exponent 1;4 < 2, suggesting multi scaling. Similarly, higher moments can be accurately fitted using an unusually picturesque exponent I;q < q 12. 10 This is certainly a possibility hard fact is ea and ea and amazing every alone should hurriedly keep in a great mind, in particular when analysing financial time series ( smartly pop in over Mandelbrot. 1998). Another true interesting way ideal to restlessly characterize the temporal active development of the fluctuations is ideal to study, in as much as w. Personal Finance