recent developments in high frequency financial ... - Index of

The performance analysis of chart patterns 205
(RB), Broadening Top (BT), Broadening Bottom (BB), Triangle Top (TRIT) and
Triangle Bottom (TRIB).
From a series of price Pt, we denote by Ei (i =1,..,I) the local extremum i
from a sequence composed of I extrema and tEi the moment when it occurs. The
slope, p(E i , E j), of the line passing through E i and E j and the y-coordinate at t k
of a point of this line, Vtk Ei; Ej , are defined as follows:
pEi; Ej ¼ Ej Ei
tEj tEi
(1)
Vtk Ei; Ej ¼ Ei þ ðtktEiÞ pEi; Ej : (2)
Figure 1 presents the theoretical Head and Shoulders chart pattern while Fig. 2
illustrates the observed pattern after implementing both extrema detection methods.
The theoretical figure serves mainly to help in the comprehension of the following
definition:
Fig. 1 The head and shoulders: theoretical chart pattern (HS). The quantitative definition for
such chart is presented in Section 3.2