

In [2]:

    
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from comparablemodels.chiarellaIori import chilori_model
from comparablemodels.GHW2008 import ghwmodel
from stockmarket.stylizedfacts import *
%matplotlib inline

Replicate comparable models

1 chiarella & Iori 2002



In [18]:

    
# set default parameters
number_of_agents = 1000
init_time = 1000
max_time = 50000
av_return_interval_min = 5
av_return_interval_max = 50 # previously Lmax
fundamental_value = 1000. # previously pf
allowed_price_steps = 0.1 # deltaP
variance_noise_forecast = 0.01 # prev sigmae
order_noise_max = 0.5 # prev kMax
order_expiration_time = 50 # prev tau
runType = 2
if runType == 0:
    fundamental_weight = 0.  # prev sigmaF
    momentum_weight = 0.    # prev sigmaM
    noise_weight = 1.       # prev sigmaN
if runType == 1:
    fundamental_weight = 1.
    momentum_weight = 0.
    noise_weight = 1.
if runType == 2:
    fundamental_weight = 1.
    momentum_weight = 10.
    noise_weight = 1.
ticks_per_day = 100



In [20]:

    
day_price, day_volume, day_return, price, returns, total_volume = chilori_model.ciarellilori2002(seed=1, max_time=max_time, 
                                                                                                 init_time=init_time, 
                                                                                                 number_of_agents=number_of_agents, 
                                                                                                 av_return_interval_min=av_return_interval_min,
                                                                                                 av_return_interval_max=av_return_interval_max, 
                                                                                                 fundamental_value=fundamental_value, 
                                                                                                 allowed_price_steps=allowed_price_steps, 
                                                                                                 variance_noise_forecast=variance_noise_forecast,
                                                                                                 order_noise_max=order_noise_max, 
                                                                                                 order_expiration_time=order_expiration_time, 
                                                                                                 fundamental_weight=fundamental_weight, 
                                                                                                 momentum_weight=momentum_weight, 
                                                                                                 noise_weight=noise_weight, 
                                                                                                 ticks_per_day=ticks_per_day)



In [15]:

    
fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(10,5))

ax1.plot(range(len(day_price)), day_price)
#ax1.set_ylim(0.02, 0.09)
ax1.set_ylabel('Closing price', fontsize='12')

ax2.plot(range(len(day_return)), day_return)
ax2.set_ylabel('Returns', fontsize='12')

ax3.plot(range(len(day_return)), [fundamental_value for x in range(len(day_return))])
#ax3.set_ylim(10, 33)
ax3.set_ylabel('Fundamental value', fontsize='12')
ax3.set_xlabel('Days', fontsize='12')

ax4.bar(range(len(day_volume)), day_volume, edgecolor='b')
ax4.set_ylabel('Volume', fontsize='12')
ax4.set_xlabel('Days', fontsize='12')

for ax in [ax1, ax2, ax3, ax4]:
    ax.ticklabel_format(axis='y', style='sci', scilimits=(-2,2))
    
#fig.savefig('chilori_dynamics.png')



In [24]:

    
pd.Series(day_return).autocorr()









    Out[24]:





-0.055607420212789055



In [25]:

    
autocorr_chilo_returns = [pd.Series(day_return).autocorr(lag=lag) for lag in range(25)]



In [27]:

    
fig, ax1 = plt.subplots(1, 1, figsize=(6,3))

# ax1.plot(autocorr_returns.index, autocorr_returns.mean(axis=1), 'k-', label='Simulation')
# ax1.fill_between(autocorr_returns.index, 
#                  autocorr_returns.mean(axis=1)+autocorr_returns.std(axis=1), 
#                  autocorr_returns.mean(axis=1)-autocorr_returns.std(axis=1), 
#                  alpha=0.3, facecolor='black')


ax1.plot(range(len(autocorr_chilo_returns)), autocorr_chilo_returns, label='Chilo')

ax1.legend(frameon=True, loc='best', framealpha=0.8)
ax1.set_ylabel('Autocorrelation', fontsize='14')
ax1.set_xlabel('Lags', fontsize='14')
#fig.savefig('auto_correlation.png')









    Out[27]:





<matplotlib.text.Text at 0x23b0f763b70>

Kurtosis:



In [32]:

    
pd.Series(day_return).kurtosis()









    Out[32]:





1.5533925745493682



In [30]:

    
print('Fat tail in Chilo (kurtosis): ', fat_tails_kurtosis(day_return))









    



Fat tail in Chilo (kurtosis):  (False, inf)

Clustered volatility



In [35]:

    
absolute_chilo_returns = pd.Series(day_return).abs()
autocorr_chilo_abs_returns = [absolute_chilo_returns.autocorr(lag=lag) for lag in range(25)]



In [36]:

    
fig, ax1 = plt.subplots(1, 1, figsize=(10,5))

#ax1.plot(range(len(autocorr_abs_returns)), autocorr_abs_returns, label='Model')
ax1.plot(range(len(autocorr_chilo_abs_returns)), autocorr_chilo_abs_returns, label='Chilo')

# ax1.plot(autocorr_returns_abs.index, autocorr_returns_abs['seed_0'], 'k-', label='Benchmark simulation')
# ax1.fill_between(autocorr_returns_abs.index, 
#                  autocorr_returns_abs.mean(axis=1)+autocorr_returns_abs.std(axis=1), 
#                  autocorr_returns_abs.mean(axis=1)-autocorr_returns_abs.std(axis=1), 
#                  alpha=0.3, facecolor='black')


ax1.legend(frameon=True, loc='best', framealpha=0.8)
ax1.set_ylabel('Autocorrelation', fontsize='14')
ax1.set_xlabel('Lag', fontsize='14')
#fig.savefig('auto_correlation_abs.png')









    Out[36]:





<matplotlib.text.Text at 0x23b1d3c1ba8>

Long memory



In [38]:

    
print('Chilo long memory (hurst)', long_memory(pd.Series(day_return), hurst, 2, 20))









    



SP500 long memory (hurst) (True, -0.024423803899288478)

Correlation between volume and volatility



In [39]:

    
window = 10



In [53]:

    
# volume
voll = pd.Series(day_volume)
# returns
roller_returns = pd.Series(returns).rolling(window)
returns_volatility = roller_returns.std(ddof=0)



In [54]:

    
print('Chilo cor vol volatility: ', returns_volatility.corr(voll))









    



Chilo cor vol volatility:  0.104320087728

Gaunersdorfer, Hommes, and Wagener (2008).

Bifurcation routes to volatility clustering under evolutionary learning. Journal of Economic Behavior and Organization, 67:27–47



In [3]:

    
price_deviation_from_fundamental, price, returns, fraction_type2 = ghwmodel.ghw_model(seed=1, simulation_time=10000, init_backward_simulated_time=4, chaos=0, risk_av_variance=1,
                       dividends=1, discount_rate=0.001, intensity_of_choice=2, fundamentalist_adaptive_parameter=1,
                       chartist_adaptive_parameter=1, bubble_sensitivity=1800, fitness_memory_strenght=0.99,
                       risk_adjustment=0, noise_std=10, init_price_dev_fundament=-400, init_type2_agents=0.5,
                       init_type2_holdings=0.5)



In [4]:

    
fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(10,5))

ax1.plot(range(len(price)), price)
#ax1.set_ylim(0.02, 0.09)
ax1.set_ylabel('Closing price', fontsize='12')

ax2.plot(range(len(returns)), returns)
ax2.set_ylabel('Returns', fontsize='12')

ax3.plot(range(len(returns)), [0 for x in range(len(returns))])
#ax3.set_ylim(10, 33)
ax3.set_ylabel('Fundamental value', fontsize='12')
ax3.set_xlabel('Days', fontsize='12')

ax4.bar(range(len(fraction_type2)), fraction_type2, edgecolor='b')
ax4.set_ylabel('Percentage chartists', fontsize='12')
ax4.set_xlabel('Days', fontsize='12')

for ax in [ax1, ax2, ax3, ax4]:
    ax.ticklabel_format(axis='y', style='sci', scilimits=(-2,2))
    
#fig.savefig('chilori_dynamics.png')

Autocorrelation



In [5]:

    
autocorr_ghw_returns = [pd.Series(returns).autocorr(lag=lag) for lag in range(25)]



In [7]:

    
fig, ax1 = plt.subplots(1, 1, figsize=(6,3))

ax1.plot(range(len(autocorr_ghw_returns)), autocorr_ghw_returns, label='Chilo')

ax1.legend(frameon=True, loc='best', framealpha=0.8)
ax1.set_ylabel('Autocorrelation', fontsize='14')
ax1.set_xlabel('Lags', fontsize='14')
#fig.savefig('auto_correlation.png')









    Out[7]:





<matplotlib.text.Text at 0x29adc8be860>

Kurtosis



In [8]:

    
pd.Series(returns).kurtosis()









    Out[8]:





0.07979982668473129



In [9]:

    
print('Fat tail in GHW (kurtosis): ', fat_tails_kurtosis(returns))









    



Fat tail in GHW (kurtosis):  (False, inf)

Clustered volatility



In [10]:

    
absolute_ghw_returns = pd.Series(returns).abs()
autocorr_ghw_abs_returns = [absolute_ghw_returns.autocorr(lag=lag) for lag in range(25)]



In [11]:

    
fig, ax1 = plt.subplots(1, 1, figsize=(10,5))

#ax1.plot(range(len(autocorr_abs_returns)), autocorr_abs_returns, label='Model')
ax1.plot(range(len(autocorr_ghw_abs_returns)), autocorr_ghw_abs_returns, label='GHW')

# ax1.plot(autocorr_returns_abs.index, autocorr_returns_abs['seed_0'], 'k-', label='Benchmark simulation')
# ax1.fill_between(autocorr_returns_abs.index, 
#                  autocorr_returns_abs.mean(axis=1)+autocorr_returns_abs.std(axis=1), 
#                  autocorr_returns_abs.mean(axis=1)-autocorr_returns_abs.std(axis=1), 
#                  alpha=0.3, facecolor='black')

ax1.legend(frameon=True, loc='best', framealpha=0.8)
ax1.set_ylabel('Autocorrelation', fontsize='14')
ax1.set_xlabel('Lag', fontsize='14')
#fig.savefig('auto_correlation_abs.png')









    Out[11]:





<matplotlib.text.Text at 0x29adca4e320>

Long memory



In [12]:

    
print('GHW long memory (hurst)', long_memory(pd.Series(returns), hurst, 2, 20))









    



GHW long memory (hurst) (True, 0.0037196380740816895)



In [ ]: