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tility estimate, we canthende.n e the volatility walk by means of the
displacement yt :
yt =

t
i=1
Oi(L) : (8)566 T.C. Mills / Physica A 338 (2004) 559 – 566
The meansquare Fuctuation, Ft , around the average displacement is given by
Ft =

Py2
t  − Pyt2 ; (9)
where Pyt = yt0+t − yt, an d· is the average over all initial steps t0. Ft follows the
scaling law Ft ˙ t and if long-range correlations are present, the scaling exponent
attains values   = 12
.
Ft was computed according to Eq. (9) for various window lengths, L=5; 10; 15; 20;
25; 50, and for t0 =1; : : : ; 100. The estimates of the exponent ranged from =0:828 ±
0:010 for L=5 to =0:845±0:012 for L=50. We cantherefore safely conclude that
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