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Code repository for Kukacka and Kristoufek (2021)

Kukacka, J., Kristoufek, L. (2021), Does parameterization affect the complexity of agent-based models?, Journal of Economic Behavior & Organization, 192, pp. 324-356, DOI.

This codebase is using the R language, and it is initialized as a Git.

It is authored by Jiri Kukacka. Question can be directed to [email protected].

Repository structure

  • simulation_gh07_cd.R master file #1. It provides R code for an illustrative replication of the results for the Gaunersdorfer and Hommes (2007) model: subsection 5.2.2. Computational setup is trivialized for personal computers. The original setup for a cluster computation to replicate results in the paper is also included. Run this file first.

  • heatmaps_gh07_cd.R master file #2. It produces the presented heat map graphics: Fig. 4, panels (c) and (d) and Fig. B.11, panel (d). It loads the output of simulation_gh07_cd.R.

  • src includes additional source scripts:

    • gh07_cd.R function generating the model output. This part of the code was downloaded in MATLAB language and translated to R from the agentFin 0.1 documentation web page [accessed 2019-10-28] by Prof. Blake LeBaron (Brandeis University, USA). Only inevitable modifications were made to link the model script to the multifractality analysis. Credit: Patrick Herb, Blake LeBaron, Axel Szmulewiez.

    • gh07_cd_MF.R function supporting evaluation of independent for-loop iterations in parallel to estimate multifractality measures.

    • MF_DFA.R set of functions needed for estimation of the multifractal spectrum, finally returning $\Delta H$ and $\Delta \alpha$ of estimated generalized Hurst exponents $H(q)$ for a given range of $q$s based on MF-DFA.

    • heatmap.2 support function for heatmaps_gh07_cd.R, downloaded from https://rdrr.io/cran/gplots/src/R/heatmap.2.R [accessed 2019-06-24].

  • replication_of_results_gh07_cd includes the files for replication of Fig. 4, panels (c) and (d) and Fig. B.11, panel (d):

    • gh07_cd.Rda data set for replication of the results in subsection 5.2.2. It must be copy-pasted to the main root to be loaded by heatmaps_gh07_cd.R to produce the following graphical outputs (for verification purposes):

      • heatmap_gh07_c_mfst.pdf actual Fig. 4, panel (c).

      • heatmap_gh07_d_conf.pdf actual Fig. 4, panel (d).

      • heatmap_gh07_diff.pdf actual Fig. B.11, panel (d).

Computational setup

  • multifractal detrended fluctuation analysis follows the setting in subsection 2.2.

  • general Monte Carlo setup follows subsection 3.1.

  • simulation_gh07_cd further follows the simulation setup in subsection 3.2. and the model benchmark setup in subsection 4.2.2.

  • heatmaps_gh07_cd.R follows the multifractality evaluation logic in subsection 3.3.

Required packages

  • install all by Pkg.add(["doParallel", "foreach", "iterators", "paralell", "gplots", "gtools"])
    • doParallel
    • foreach
    • iterators
    • paralell
    • gplots
    • gtools

Variables and function arguments

  • general simulation setup:
    • runs number of independent Monte Carlo runs for each experiment.
    • burn number of burn-in periods to discard.
    • obs number of periods desired.
    • metrics actual number of estimates generated in gh07_cd_MF.R.
  • parameterization:
    • k_val benchmark parameterization for $\psi$, associated with the vertical axis of heatmaps.
    • j_val benchmark parameterization for $\gamma$, associated with the horizontal axis of heatmaps.
    • kk,kkk vertical position in the grid.
    • jj,jjj horizontal position in the grid.
  • multifractal spectrum estimation setup:
    • smin minimum scale to consider for the scaling law.
    • smax maximum scale to consider for the scaling law.
    • sstep step length for scales between smin and smax.
    • qmax maximum moment $q$ for estimation of the multifractal spectrum.
    • qmin minimum moment $q$ for estimation of the multifractal spectrum.
    • qstep step length for moments between qmin and qmax.