asycaus — Asymmetric Granger-Causality Suite¶

Full demo on real-world data: crude-oil shocks → S&P 500¶

Author: Dr Merwan Roudane  ·  merwanroudane920@gmail.com

Links:

  • GitHub: https://github.com/merwanroudane/asycaus
  • PyPI: https://pypi.org/project/asycaus/
  • Stata twin (SSC): ssc install asycaus

This notebook runs every test in the asycaus library on a real dataset and saves all tables and figures into docs/tables/ and docs/figures/ so they can be reproduced and embedded in the GitHub Pages site.

The empirical setup follows Hatemi-J (2012): do positive vs negative shocks in crude-oil prices have different causal effects on the world's largest stock market?

1. Setup¶

In [1]:
import os, warnings
warnings.filterwarnings('ignore')

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import yfinance as yf

import asycaus
print('asycaus version:', asycaus.__version__)
print('Author         :', asycaus.__author__, '<' + asycaus.__email__ + '>')
print('GitHub         :', asycaus.__url__)

# Where to drop tables and figures so docs/ embeds them automatically
ROOT = os.path.abspath(os.path.join(os.getcwd(), os.pardir)) if os.path.basename(os.getcwd()) == 'examples' else os.getcwd()
FIG_DIR = os.path.join(ROOT, 'docs', 'figures')
TBL_DIR = os.path.join(ROOT, 'docs', 'tables')
os.makedirs(FIG_DIR, exist_ok=True)
os.makedirs(TBL_DIR, exist_ok=True)
print('FIG_DIR:', FIG_DIR)
print('TBL_DIR:', TBL_DIR)

asycaus version: 1.0.0
Author         : Dr Merwan Roudane <merwanroudane920@gmail.com>
GitHub         : https://github.com/merwanroudane/asycaus
FIG_DIR: C:\Users\HP\Documents\xtpmg\asycaus\asycaus_py\docs\figures
TBL_DIR: C:\Users\HP\Documents\xtpmg\asycaus\asycaus_py\docs\tables

2. Real data — WTI crude oil and S&P 500¶

We download daily closing prices from Yahoo Finance (2015–2024) and convert to monthly log levels, the standard frequency for causality studies in finance.

In [2]:
raw = yf.download(['CL=F', '^GSPC'], start='2015-01-01', end='2024-12-31',
                  progress=False, auto_adjust=True)['Close']
raw = raw.rename(columns={'CL=F': 'oil', '^GSPC': 'sp500'}).dropna()

# Monthly frequency, end-of-month closes -> log levels
monthly = raw.resample('M').last().apply(np.log).dropna()
monthly.columns = ['ln_oil', 'ln_sp500']
print(monthly.shape, 'monthly observations')
monthly.head()

(120, 2) monthly observations
Out[2]:
ln_oil ln_sp500
Date
2015-01-31 3.876189 7.598394
2015-02-28 3.907211 7.651833
2015-03-31 3.862833 7.634284
2015-04-30 4.088159 7.642769
2015-05-31 4.099332 7.653205
In [3]:
fig, axes = plt.subplots(2, 1, figsize=(10, 6), sharex=True)
axes[0].plot(monthly.index, monthly['ln_oil'], color='#1f3a93', lw=1.8)
axes[0].set_title('log WTI crude oil (CL=F)', fontweight='bold')
axes[0].grid(alpha=0.3)
axes[1].plot(monthly.index, monthly['ln_sp500'], color='#27ae60', lw=1.8)
axes[1].set_title('log S&P 500 (^GSPC)', fontweight='bold')
axes[1].grid(alpha=0.3)
plt.suptitle('Monthly data, log levels — 2015 to 2024',
             y=1.02, fontsize=13, fontweight='bold')
plt.tight_layout()
plt.savefig(os.path.join(FIG_DIR, '00_data.png'), bbox_inches='tight', dpi=170)
plt.show()
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3. Cumulative positive / negative shocks (Granger-Yoon 2002)¶

Each variable is split into the cumulative sum of its positive innovations and the cumulative sum of its negative innovations. This is the heart of the asymmetric causality framework: instead of testing whether oil causes sp500, we test whether positive oil shocks cause positive S&P shocks (or any combination).

In [4]:
y = monthly['ln_sp500'].to_numpy()   # dependent variable
x = monthly['ln_oil'].to_numpy()     # candidate cause
Y = np.column_stack([y, x])

C_pos = asycaus.pos_neg_components(Y, positive=True)
C_neg = asycaus.pos_neg_components(Y, positive=False)

comp = pd.DataFrame(
    np.hstack([C_pos, C_neg]),
    columns=['cum_pos_sp500', 'cum_pos_oil', 'cum_neg_sp500', 'cum_neg_oil'],
    index=monthly.index[1:],
)
comp.head()
Out[4]:
cum_pos_sp500 cum_pos_oil cum_neg_sp500 cum_neg_oil
Date
2015-02-28 0.053439 0.031023 0.000000 0.000000
2015-03-31 0.053439 0.031023 -0.017549 -0.044379
2015-04-30 0.061924 0.256349 -0.017549 -0.044379
2015-05-31 0.072360 0.267522 -0.017549 -0.044379
2015-06-30 0.072360 0.267522 -0.038785 -0.058239
In [5]:
fig, axes = plt.subplots(2, 1, figsize=(10, 6), sharex=True)
axes[0].plot(comp.index, comp['cum_pos_oil'],   color='#27ae60', label='cum POS oil',   lw=1.8)
axes[0].plot(comp.index, comp['cum_neg_oil'],   color='#c0392b', label='cum NEG oil',   lw=1.8)
axes[0].set_title('Cumulative positive vs negative oil shocks', fontweight='bold')
axes[0].legend(); axes[0].grid(alpha=0.3)
axes[1].plot(comp.index, comp['cum_pos_sp500'], color='#27ae60', label='cum POS S&P',   lw=1.8)
axes[1].plot(comp.index, comp['cum_neg_sp500'], color='#c0392b', label='cum NEG S&P',   lw=1.8)
axes[1].set_title('Cumulative positive vs negative S&P shocks', fontweight='bold')
axes[1].legend(); axes[1].grid(alpha=0.3)
plt.suptitle('Granger-Yoon (2002) decomposition', y=1.02, fontsize=13, fontweight='bold')
plt.tight_layout()
plt.savefig(os.path.join(FIG_DIR, '01_components.png'), bbox_inches='tight', dpi=170)
plt.show()
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4. Static asymmetric causality — Hatemi-J (2012)¶

Modified Wald in a VAR(p+1) on the cumulative components, with bootstrap critical values that use the leverage-adjustment of Hacker & Hatemi-J (2006, 2012). The bootstrap is robust to non-normality and ARCH — both common in oil and equity returns.

In [6]:
static = asycaus.static(y, x, shock='both', max_lag=6,
                        boot=500, seed=12345, plot=False)
static.table.to_csv(os.path.join(TBL_DIR, '01_static.csv'))
fig = static.plot(save=os.path.join(FIG_DIR, '02_static.png'))

────────────────────────────────── Asymmetric Causality Test -- Hatemi-J (2012) ───────────────────────────────────

H0: x does not Granger-cause y

Lag selection: HJC    Augmentation lags: 1    Bootstrap reps: 500    Sample: 119

           Asymmetric Causality Test  --  Hatemi-J (2012)            
┏━━━━━━━━━━┳━━━━━━━━┳━━━━━┳━━━━━━━━┳━━━━━━━━┳━━━━━━━━┳━━━━━━━━┳━━━━━┓
┃ Shock    ┃   Wald ┃ Lag ┃  Asy p ┃ CV 10% ┃  CV 5% ┃  CV 1% ┃ Sig ┃
┡━━━━━━━━━━╇━━━━━━━━╇━━━━━╇━━━━━━━━╇━━━━━━━━╇━━━━━━━━╇━━━━━━━━╇━━━━━┩
│ Positive │ 0.0482 │   1 │ 0.8261 │ 0.3594 │ 0.5163 │ 0.9617 │     │
│ Negative │ 0.2710 │   1 │ 0.6027 │ 0.3619 │ 0.4991 │ 0.9467 │     │
└──────────┴────────┴─────┴────────┴────────┴────────┴────────┴─────┘

Significance: * 10%  ** 5%  *** 1%  (leverage-adjusted bootstrap CVs)
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5. Dynamic asymmetric causality — Hatemi-J (2021)¶

The static test gives a single Wald statistic for the whole sample, but the oil-stock relationship is known to be unstable (Gulf War, 2014–16 oil glut, COVID crash, 2022 invasion of Ukraine). We re-estimate the test on a rolling window of size

$$S = \left\lceil T\bigl(0.01 + 1.8/\sqrt T\bigr)\right\rceil$$

(Phillips, Shi & Yu 2015) for positive shocks, then for negative shocks. The resulting Wald time-series shows precisely when asymmetric causation turns on and off.

In [7]:
dyn_pos = asycaus.dynamic(y, x, shock='pos', mode='rolling',
                          max_lag=3, boot=120, seed=12345,
                          plot=False, progress=False)
dyn_pos.table.to_csv(os.path.join(TBL_DIR, '02_dynamic_pos.csv'))
fig = dyn_pos.plot(save=os.path.join(FIG_DIR, '03_dynamic_pos.png'))

───────────────────────────────── Dynamic Asymmetric Causality -- Hatemi-J (2021) ─────────────────────────────────

H0: x does not Granger-cause y  (pos shocks)

Mode: Rolling window    Window: 21  (PSY min=21)    Lag IC: HJC    Boot: 120

        Dynamic Asymmetric Causality -- Hatemi-J (2021)         
┏━━━━━━━━┳━━━━━┳━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━┓
┃ SS End ┃ Lag ┃    Wald ┃ CV 10% ┃   CV 5% ┃   CV 1% ┃ W/CV5% ┃
┡━━━━━━━━╇━━━━━╇━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━┩
│     21 │   1 │  0.0157 │ 0.3887 │  0.5042 │  1.0244 │ 0.0312 │
│     31 │   3 │ 12.0298 │ 9.1808 │ 18.0657 │ 30.9636 │ 0.6659 │
│     41 │   1 │  0.2129 │ 0.3674 │  0.5388 │  0.8526 │ 0.3950 │
│     51 │   1 │  0.1728 │ 0.7829 │  1.3274 │  2.1312 │ 0.1302 │
│     61 │   1 │  0.0001 │ 0.6050 │  0.9522 │  1.9664 │ 0.0001 │
│     71 │   1 │  0.0060 │ 0.3144 │  0.4810 │  3.4088 │ 0.0125 │
│     81 │   3 │  0.4177 │ 3.2435 │  5.2694 │ 10.1631 │ 0.0793 │
│     91 │   2 │  4.1522 │ 4.2422 │  7.2437 │ 12.5349 │ 0.5732 │
│    101 │   2 │  0.1800 │ 6.0706 │ 10.8703 │ 20.2916 │ 0.0166 │
│    111 │   1 │  0.1301 │ 1.5982 │  2.5171 │  3.4851 │ 0.0517 │
│    119 │   3 │  0.6511 │ 7.2811 │  9.0812 │ 18.6690 │ 0.0717 │
└────────┴─────┴─────────┴────────┴─────────┴─────────┴────────┘

Subsamples rejecting H0: 0 at 1%,  1 at 5%,  6 at 10%   (of 99 windows)
No description has been provided for this image
In [8]:
dyn_neg = asycaus.dynamic(y, x, shock='neg', mode='rolling',
                          max_lag=3, boot=120, seed=12345,
                          plot=False, progress=False)
dyn_neg.table.to_csv(os.path.join(TBL_DIR, '03_dynamic_neg.csv'))
fig = dyn_neg.plot(save=os.path.join(FIG_DIR, '04_dynamic_neg.png'))

───────────────────────────────── Dynamic Asymmetric Causality -- Hatemi-J (2021) ─────────────────────────────────

H0: x does not Granger-cause y  (neg shocks)

Mode: Rolling window    Window: 21  (PSY min=21)    Lag IC: HJC    Boot: 120

        Dynamic Asymmetric Causality -- Hatemi-J (2021)         
┏━━━━━━━━┳━━━━━┳━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━┓
┃ SS End ┃ Lag ┃   Wald ┃  CV 10% ┃   CV 5% ┃   CV 1% ┃ W/CV5% ┃
┡━━━━━━━━╇━━━━━╇━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━┩
│     21 │   1 │ 0.6923 │  0.3222 │  0.5034 │  0.8023 │ 1.3753 │
│     31 │   2 │ 0.1215 │  3.3492 │  5.6978 │ 15.1941 │ 0.0213 │
│     41 │   1 │ 0.0000 │  0.5383 │  1.2310 │  3.0147 │ 0.0000 │
│     51 │   1 │ 1.7133 │  0.5635 │  0.7788 │  1.6070 │ 2.2001 │
│     61 │   1 │ 1.4152 │  0.5019 │  0.7141 │  2.0098 │ 1.9819 │
│     71 │   3 │ 6.7229 │ 16.6613 │ 34.8853 │ 81.5259 │ 0.1927 │
│     81 │   2 │ 1.2522 │  3.3061 │  4.8712 │ 10.8622 │ 0.2571 │
│     91 │   2 │ 3.0784 │  6.5420 │ 10.4382 │ 20.7934 │ 0.2949 │
│    101 │   2 │ 2.1425 │  3.6202 │  5.3668 │ 17.3089 │ 0.3992 │
│    111 │   2 │ 1.8291 │  3.1406 │  5.0400 │  7.1745 │ 0.3629 │
│    119 │   2 │ 0.4468 │  5.5704 │  6.8184 │ 13.7273 │ 0.0655 │
└────────┴─────┴────────┴─────────┴─────────┴─────────┴────────┘

Subsamples rejecting H0: 7 at 1%,  20 at 5%,  24 at 10%   (of 99 windows)
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6. Fourier-augmented asymmetric TY — Nazlioglu et al. (2016) / Pata (2020)¶

Smooth structural breaks of unknown number, timing and form are absorbed by sine/cosine terms inserted into the VAR. The frequency k* is chosen automatically over k ∈ {1,…,k_max}.

In [9]:
fr = asycaus.fourier(y, x, shock='both', kmax=4, form='single',
                     max_lag=6, plot=False)
fr.table.to_csv(os.path.join(TBL_DIR, '04_fourier.csv'))
fig = fr.plot(save=os.path.join(FIG_DIR, '05_fourier.png'))

Fourier Asymmetric TY Causality (Nazlioglu et al. 2016)
┏━━━━━━━━━━┳━━━━━━━━━━┳━━━━━┳━━━━┳━━━━━━━━┳━━━━━┳━━━━━┓
┃ Shock    ┃     Wald ┃ Lag ┃ k* ┃  Asy p ┃ Obs ┃ Sig ┃
┡━━━━━━━━━━╇━━━━━━━━━━╇━━━━━╇━━━━╇━━━━━━━━╇━━━━━╇━━━━━┩
│ Positive │ 101.5157 │   1 │  1 │ 0.0000 │ 119 │ *** │
│ Negative │ 332.3207 │   1 │  3 │ 0.0000 │ 119 │ *** │
└──────────┴──────────┴─────┴────┴────────┴─────┴─────┘
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7. Frequency-domain asymmetric causality — Bahmani-Oskooee, Chang & Ranjbar (2016)¶

Breitung-Candelon (2006) spectral causality applied separately to the cumulative positive and negative components. For each angular frequency $\omega \in (0, \pi]$ we report a $\chi^2(2)$ Wald statistic. The plot shows the Wald-vs-frequency curve with 1%, 5%, 10% critical lines — the canonical Bahmani-Oskooee presentation.

In [10]:
sp = asycaus.spectral(y, x, shock='both', nfreq=50, max_lag=6, plot=False)
sp.summary.to_csv(os.path.join(TBL_DIR, '05_spectral_summary.csv'))
sp.table.to_csv(os.path.join(TBL_DIR, '05_spectral_full.csv'), index=False)
fig = sp.plot(save=os.path.join(FIG_DIR, '06_spectral.png'))

           Asymmetric Frequency-Domain Causality (BCRanjbar 2016)           
┏━━━━━━━━━━┳━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━┓
┃ Shock    ┃ Lag ┃ n_reject_1% ┃ n_reject_5% ┃ n_reject_10% ┃ % reject @5% ┃
┡━━━━━━━━━━╇━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━┩
│ Positive │   1 │           0 │           0 │            0 │        0.00% │
│ Negative │   1 │           0 │           0 │            0 │        0.00% │
└──────────┴─────┴─────────────┴─────────────┴──────────────┴──────────────┘
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8. Quantile asymmetric causality — Fang, Wang, Shieh & Chung (2026)¶

Tests whether oil causes the S&P 500 at different quantiles of the S&P 500's distribution — i.e., is the causal effect bigger in bull markets, in bear markets, or near the median? Optionally, smooth structural breaks are first removed via a cumulative Fourier basis (fourier=True).

In [11]:
q = asycaus.quantile(y, x, shock='both',
                     quantiles=(0.1, 0.25, 0.5, 0.75, 0.9),
                     max_lag=4, fourier=True, kmax=2, plot=False)
q.table.to_csv(os.path.join(TBL_DIR, '06_quantile.csv'), index=False)
fig = q.plot(save=os.path.join(FIG_DIR, '07_quantile.png'))

 Quantile Asymmetric Causality (Fang et al. 2026) 
┏━━━━━━━━━━┳━━━━━━┳━━━━━━━━━┳━━━━━┳━━━━━━━━┳━━━━━┓
┃ Shock    ┃  tau ┃    Wald ┃ Lag ┃  Asy p ┃ Sig ┃
┡━━━━━━━━━━╇━━━━━━╇━━━━━━━━━╇━━━━━╇━━━━━━━━╇━━━━━┩
│ Positive │ 0.10 │  0.3606 │   1 │ 0.5482 │     │
│ Positive │ 0.25 │  0.5812 │   1 │ 0.4459 │     │
│ Positive │ 0.50 │  0.1031 │   1 │ 0.7482 │     │
│ Positive │ 0.75 │  0.6503 │   1 │ 0.4200 │     │
│ Positive │ 0.90 │ 13.9727 │   1 │ 0.0002 │ *** │
│ Negative │ 0.10 │ 13.4482 │   1 │ 0.0002 │ *** │
│ Negative │ 0.25 │  1.9448 │   1 │ 0.1631 │     │
│ Negative │ 0.50 │  0.2107 │   1 │ 0.6462 │     │
│ Negative │ 0.75 │  0.6970 │   1 │ 0.4038 │     │
│ Negative │ 0.90 │  0.0264 │   1 │ 0.8709 │     │
└──────────┴──────┴─────────┴─────┴────────┴─────┘
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9. Efficient asymmetric tests — Hatemi-J (2024)¶

Joint SUR estimation of the positive and negative systems. Four hypotheses are produced in one shot:

# Null
1 No causality via positive shocks
2 No causality via negative shocks
3 Joint no causality (1 AND 2)
4 Positive = Negative causal coefficients ← formal asymmetry test
In [12]:
eff = asycaus.efficient(y, x, max_lag=6, plot=False)
eff.table.to_csv(os.path.join(TBL_DIR, '07_efficient.csv'))
fig = eff.plot(save=os.path.join(FIG_DIR, '08_efficient.png'))

       Efficient Asymmetric Causality (SUR)  --  Hatemi-J (2024)        
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━┳━━━━┳━━━━━━━━┳━━━━━━━━━━━━━━━━┓
┃ Null hypothesis             ┃    Wald ┃ df ┃  Asy p ┃ Decision       ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━╇━━━━╇━━━━━━━━╇━━━━━━━━━━━━━━━━┩
│ No causality via POS shocks │  0.5543 │  1 │ 0.4565 │ Fail to reject │
│ No causality via NEG shocks │ 12.9621 │  1 │ 0.0003 │ Reject         │
│ Joint no causality          │ 14.3627 │  2 │ 0.0008 │ Reject         │
│ POS = NEG causal effects    │ 10.5752 │  1 │ 0.0011 │ Reject         │
└─────────────────────────────┴─────────┴────┴────────┴────────────────┘
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10. Full battery + unified summary¶

A single asycaus.all_tests(...) call runs everything above and prints one unified row per (test × shock).

In [13]:
battery = asycaus.all_tests(y, x, max_lag=4, boot=200,
                            skip_dynamic=True, skip_spectral=False,
                            plot=False)
battery.summary.to_csv(os.path.join(TBL_DIR, '08_battery_summary.csv'), index=False)
battery.summary

==============================================================================
                         ASYMMETRIC CAUSALITY BATTERY                         
                          Author: Dr Merwan Roudane                           
==============================================================================
 Direction tested:  causvar -> depvar

[1/6] Static Asymmetric Causality (Hatemi-J 2012)...

[2/6] Fourier Asymmetric TY (Nazlioglu et al. 2016)...

[3/6] Efficient Asymmetric (Hatemi-J 2024)...

[4/6] Spectral Asymmetric (Bahmani-Oskooee et al. 2016)...

[5/6] Quantile Asymmetric (Fang et al. 2026)...

                       UNIFIED ASYMMETRIC CAUSALITY SUMMARY                        
╔══════════════════════════════╤═══════╤═══════════════╤═════════╤════════════════╗
║ Test                         │ Shock │     Statistic │ p-value │ Decision       ║
╟──────────────────────────────┼───────┼───────────────┼─────────┼────────────────╢
║ Static (Hatemi-J 2012)       │  Pos  │        0.0482 │  0.8261 │ Fail to reject ║
║ Static (Hatemi-J 2012)       │  Neg  │        0.2710 │  0.6027 │ Fail to reject ║
║ Fourier (Nazlioglu 2016)     │  Pos  │      101.5157 │  0.0000 │ Reject         ║
║ Fourier (Nazlioglu 2016)     │  Neg  │      332.3207 │  0.0000 │ Reject         ║
║ Efficient Pos only (HJ 2024) │  Pos  │        0.5543 │  0.4565 │ Fail to reject ║
║ Efficient Neg only (HJ 2024) │  Neg  │       12.9621 │  0.0003 │ Reject         ║
║ Efficient Joint (HJ 2024)    │ both  │       14.3627 │  0.0008 │ Reject         ║
║ Efficient Pos=Neg (HJ 2024)  │ diff  │       10.5752 │  0.0011 │ Reject         ║
║ Spectral (BCRanjbar 2016)    │  Pos  │   0.00% freq. │  0.0000 │ Fail to reject ║
║ Spectral (BCRanjbar 2016)    │  Neg  │   0.00% freq. │  0.0000 │ Fail to reject ║
║ Quantile (Fang et al. 2026)  │  Pos  │  0.00% quant. │  0.0000 │ Fail to reject ║
║ Quantile (Fang et al. 2026)  │  Neg  │ 20.00% quant. │  0.2000 │ Reject at some ║
╚══════════════════════════════╧═══════╧═══════════════╧═════════╧════════════════╝
         Decision at 5% level.  Spectral/quantile rows report fraction of          
                         frequencies/quantiles rejecting.
Out[13]:
Test Shock Statistic p-value Decision
0 Static (Hatemi-J 2012) Pos 0.048244 8.261478e-01 Fail to reject
1 Static (Hatemi-J 2012) Neg 0.271009 6.026560e-01 Fail to reject
2 Fourier (Nazlioglu 2016) Pos 101.515733 7.089810e-24 Reject
3 Fourier (Nazlioglu 2016) Neg 332.320745 3.001451e-74 Reject
4 Efficient Pos only (HJ 2024) Pos 0.55434 4.565498e-01 Fail to reject
5 Efficient Neg only (HJ 2024) Neg 12.962146 3.178526e-04 Reject
6 Efficient Joint (HJ 2024) both 14.362713 7.606353e-04 Reject
7 Efficient Pos=Neg (HJ 2024) diff 10.575201 1.146148e-03 Reject
8 Spectral (BCRanjbar 2016) Pos 0.00% freq. 0.000000e+00 Fail to reject
9 Spectral (BCRanjbar 2016) Neg 0.00% freq. 0.000000e+00 Fail to reject
10 Quantile (Fang et al. 2026) Pos 0.00% quant. 0.000000e+00 Fail to reject
11 Quantile (Fang et al. 2026) Neg 20.00% quant. 2.000000e-01 Reject at some

11. Conclusion¶

The asycaus library produces a clean, end-to-end asymmetric-causality analysis on real financial data with one consistent API, professional tables and publication-quality plots.

Every artifact above is saved under docs/figures/ and docs/tables/ for embedding in the GitHub Pages site.

Citation

Roudane, M. (2026). asycaus: Asymmetric Granger-causality suite for Python. Version 1.0.0. https://github.com/merwanroudane/asycaus

Companion Stata package on SSC: ssc install asycaus