Add Li-Mak (1994) portmanteau test for ARCH effects in standardized residuals

[hass-nation]

Summary

Closes #405.

Adds li_mak_test(lags, fitdf) to ARCHModelFixedResult, implementing the Li & Mak (1994) diagnostic test for remaining ARCH effects.

The test applies the Ljung-Box portmanteau statistic to squared standardized residuals e_t² = (r_t / σ_t)² and corrects the degrees of freedom for GARCH parameter estimation uncertainty:

Q*(m) = T(T+2) · Σₖ₌₁ᵐ r̂ₖ² / (T−k)   ~  χ²(m − fitdf)

where r̂ₖ is the k-th autocorrelation of e_t² and fitdf defaults to volatility.num_params − 1 (all estimated lag parameters, excluding the constant ω).

Why this is different from arch_lm_test

	arch_lm_test	li_mak_test
Residuals tested	raw r_t	standardized r_t / σ_t
Test statistic	LM/OLS (T · R²)	Ljung-Box
df correction	none	− fitdf
Null hypothesis	residuals are homoskedastic	GARCH model captures all variance clustering

arch_lm_test detects heteroskedasticity in raw residuals; li_mak_test checks whether the fitted GARCH model has adequately removed all conditional variance structure.

Parameters

• lags — number of autocorrelation lags (default: ⌈1.2 · T^{1/4}⌉, same as arch_lm_test)
• fitdf — df correction (default: volatility.num_params − 1; pass fitdf=0 for uncorrected Ljung-Box)

Tests

3 new test functions in arch/tests/univariate/test_mean.py:

• test_li_mak — default call, explicit lags, fitdf=0 cross-check against manual Ljung-Box, comparison with arch_lm_test, custom fitdf
• test_li_mak_constant_variance — ConstantVariance model gives fitdf=0
• test_li_mak_pval_structure — p-value, critical values, repr consistency

All existing tests pass unchanged.

Reference

Li, W. K. and Mak, T. K. (1994). On the Squared Residual Autocorrelations in Non-Linear Time Series with Conditional Heteroskedasticity. Journal of Time Series Analysis, 15(6), 627–636. https://doi.org/10.1111/j.1467-9892.1994.tb00217.x

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Codecov Report

❌ Patch coverage is 97.10145% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 99.52%. Comparing base (543f44c) to head (d2331d4).

Files with missing lines	Patch %	Lines
arch/univariate/base.py	90.90%	1 Missing and 1 partial ⚠️

Additional details and impacted files

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- Coverage   99.54%   99.52%   -0.03%     
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  Lines       15818    15887      +69     
  Branches     1294     1298       +4     
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+ Hits        15746    15811      +65     
- Misses         38       40       +2     
- Partials       34       36       +2     

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