Mathematical and Statistical Methods for Actuarial Sciences and Finance

(Nora) #1
Financial time series and neural networks in a minority game context 161

(^57005101520253035404550)
580
590
600
610
620
630
640
650
M
Predictions
Total observations 1240
η=0.23
Fig. 7.Number of corrected predictions as a function ofMin the case of Nikkei 225. The
maximum is reached forM= 3
this market different. On the other hand the case of S&P500, DJ Eurostoxx 50, Dow
Jones, Mibtel and Nikkei 225 is completely different, as these markets’ investors
consider only the very recent past sinceM = 2 −4 and the neural network can
predict slightly more than 50% of entries. This can lead us to consider these time
series as randomly generated and so consider these markets more efficient. In both
cases the neural network shows the presence of a valueMfor which the number of
predictions is maximum and this is the number of past entries that agents consider in
order to make decisions. This information is derived directly from the data.


References



  1. Arthur, W.B.: Inductive reasoning and bounded rationality. Am. Econ. Rev. 84,406–411
    (1994)

  2. Bachelier, L.: Theorie de la speculation. Paris (1900). Reprinted by MIT Press, Cambridge
    (1964)

  3. Bernaschi, M., Grilli, L., Vergni, D.: Statistical analysis of fixed income market. Phys. A
    Stat. Mech. Appl. 308, 381–390 (2002)

  4. Cavagna A.: Irrelevance of memory in the minority game. Phys. Rev. E, 59:R3783 (1999)

  5. Challet, D.: Inter-pattern speculation: beyond minority, majority and $-games. cond-
    mat/05021405 (2005)

  6. Challet, D., Chessa, A., Marsili, M., Zhang, Y.-C.: From Minority Games to real markets.
    cond-mat/0011042 (2000)

  7. Coolen, A.C.C.: Generating funcional analysis of Minority Games with real market his-
    tories. cond-mat/0410335 (2004)

Free download pdf