Information Technology Reference
In-Depth Information
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0
500
1000
1500
2000
2500
t
Fig. 3.
The time evolution of
Ψ
(
t
)for
λ
-GCMG with
N
=1and
S
=16
pairwise different strategies from RSS.
Red dashed line corresponds to
λ
=0
.
7,
solid blue line corresponds to
λ
=0
.
97 ,
green dotted line corresponds to
λ
=1.
Fig. 4.
The
Ψ
(
t
)attime
t
= 3000 for
λ
=16pair-
wise different strategies from RSS and
λ
=0
.
97. Error bars correspond to one
standard deviation calculated over 10 re-
alizations.
-GCMG with
N
=1,
S
because MG predicts only the sign and not a value of sample. We assume that
the exact form of function
f
is unknown and it can evolve over time. In case of
the model in Fig. 1, the returns
r
(
t
) correspond to signals
y
(
t
). Considering the
second term
ξ
(
t
), there are many various exogenous factors, e.g. inflation, com-
panies annual balances, etc. Investors react on them in various ways. Therefore,
instead of considering reactions of individuals separately, we assume that signals
of
ξ
(
t
) are instances of IID process, with mean value equal to zero. The assump-
tion seems more reasonable in the case of intraday data than for the end-of-day
data [11]. This suggests that the majority in high-frequency data movements
can be potentially self-generated, while the lower frequencies are dominated by
exogenous factors.
λ
6.2 Application of
-GCMG
We look for a
λ
-GCMG model being able to estimate function
f
in Eq. (8). Using
our previous results, we set the following parameter values:
N
=1,
λ
=0
.
97 and
the number of strategies covering the RSS. The
m
value should be chosen from
the range 1
10 [13]. The precise choice of
m
requires some additional analysis.
If we take a look at Fig. 5, where the
λ
-GCMG is applied as a predictor to
FW20 time series i.e. futures contracts on WIG20 index that is the index of the
twenty largest companies on the Warsaw Stock Exchange, then it is seen that
better correctness is achieved for lower
m
i.e.
m
= 1. This result, at least at
first sight, seems to be counter-intuitive. The RSS of higher order includes all
strategies of RSS of lower order and additionally introduces the same number of
extra strategies. The explanation is that for higher
m
the additional strategies,
although do not capture properly dependencies, get from time to time higher
−
