Information Technology Reference
In-Depth Information
Fig. 3.
Price behavior for varying
λ
in ExAG
becomes, the fewer the number of direct actions occur. Thus, the ratio of trend-followers
is high for
λ
=0
.
0001
and that of contrarians is high for
λ
=0
.
01
.
In addition, Figure 4 shows the skewness and the kurtosis for varying the constant
λ
,
where the skewness (
α
3
) and the kurtosis (
α
4
) are defined as
N
N
x
)
3
Nσ
3
x
)
4
Nσ
4
(
x
i
−
(
x
i
−
α
3
=
and
α
4
=
,
i
=1
i
=1
respectively, for time series variable
x
i
and its average
x
. If the skewness is negative
(respectively, positive), the left (respectively, right) tail of a distribution is longer. A
high kurtosis distribution has a sharper peak and longer, fatter tails, while a low kurtosis
distribution has a more rounded peak and shorter, thinner tails. In other words, the more
the patterns of price fluctuation occur, the smaller the kurtosis becomes. Thus, if
λ
is
small and the reversal movements of contrarians are rare, the kurtosis becomes large.
On the other hand, if we vary
K
−
with keeping
K
+
= 500
, the kurtosis is distributed
as shown in Figure 5, where a regression curve is depicted.
From the observation above, we set
λ
=0
.
001
,
K
−
=50
and
K
+
= 500
in what
follows.
Fig. 5.
Kurtosis vs
K
−
in ExAG
Fig. 4.
Skewness / kurtosis vs
λ
in ExAG
