Soft Computing

, Volume 21, Issue 7, pp 1693–1708

Predicting agent-based financial time series model on lattice fractal with random Legendre neural network

Methodologies and Application

DOI: 10.1007/s00500-015-1874-3

Cite this article as:
Pei, A., Wang, J. & Fang, W. Soft Comput (2017) 21: 1693. doi:10.1007/s00500-015-1874-3


An agent-based financial price model is developed by percolation system on the Sierpinski carpet lattice, in an attempt to reproduce and investigate fluctuation behaviors of price changes in the financial market. The percolation theory is usually used to describe the behaviors of connected clusters in a random graph, and the Sierpinski carpet lattice is an infinitely ramified fractal. We forecast and investigate the stock prices of the financial model by an improved Legendre neural network–Legendre neural network with random time strength function (LeNNRT). To test the LeNNRT and study the fluctuation behaviors of the stock prices on different time lag, the k-day moving average of Shanghai Composite Index and the simulated price series of the proposed model are predicted by the LeNNRT model. We exhibit the predictive results and compare the forecasting accuracies with different values of k for both the real data and the simulated data.


Predicting Sierpinski carpet Financial price model Legendre neural network Random time strength function 

Funding information

Funder NameGrant NumberFunding Note
National Natural Science Foundation of China
  • 71271026
National Natural Science Foundation of China
  • 10971010
Fundamental Research Funds for the Central Universities
  • 2015JBM124

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceBeijing Jiaotong UniversityBeijingPeople’s Republic of China
  2. 2.Department of Finance, School of Economics and ManagementBeijing Jiaotong UniversityBeijingPeople’s Republic of China

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