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it: the feedback effect and the quenched disorder [4]. The incorporated feedback
effect couples input and output signals in such a way that a minority decision at
time
t
constitutes the basis for future agents' decisions. The quenched disorder
is related to an initial, random realization of agents' strategies in their strategy
space. In theoretical papers [3] it is discussed how the feedback mechanism affects
observed behavior of MGs. For us it is important that the lack of the feedback
does not influence the population's predictive power which is exclusively driven
by the quenched disorder.
Some other authors applied the model to the exogenous, real data, assuming
an existence of patterns in these data and using MG as a predictor of its future
value [11,10,8,9,7,12]. Although the MG-based predictor is able to forecast any
time series assuming that the length of patterns suits agents' strategies, the com-
monly used exogenous time series are those related to asset prices. In [11,10] the
authors performed an experiment where the time series of hourly Dollar $/Yen
exchange rate was examined. Although the results are interesting and inspiring,
there is nearly no details about the conditions of the experiment. Such parame-
ters like
m
,
S
,
N
are not revealed, making the results unreproducible.
The prediction method used in Ref. [10] was further developed by others
[8,9,7,12]. Above methods of optimization are based on comparison between two
distributions of signals, i.e. the exogenous and predicted one. If the distributions
are mutually close to each other, the model is considered as a well fitted to the
object. As we presented in section 5, this technique, although interesting, does
not assure that the success rate of the one-step prediction is maximized.
4 The Model
Here, we present the details about our implemented predictor and its configura-
tion. We used, the Grand Canonical extension of the MG in all our simulations.
4.1 Grand Canonical Extension
In the standard MG all agents have to play at each time step
t
,evenifallof
their strategies are unprofitable. Looking for analogies to financial markets we
see that in real life investors behave differently. If for some of them trading is
not profitable, they withdraw from the market. Formally, staying apart from the
market is realized by
zero strategy
. This additional strategy, marked as
α
i
,maps
all
μ
to the
a
i
= 0 and does not influence the aggregate demand
A
. We assume
a constant risk-free interest rate as being equal to
U
α
0
i
(
t
)=
U
α
0
i
=0.
4.2 Configuration
Technically, the predictor works according to the diagram presented in Fig. 1.
The object that we suppose to model is treated as a black-box stimulated by (i)
the vector of previously generated signs of samples sgn
y
(
t
1)
=[sgn
y
(
t
−
−
1)
...
sgn
y
(
t
n
)
], where
n>
1, and (ii) the external information
ξ
(
t
). We
−
