[bashtage]

Makes the ADF t-test and z-test tables consistent with each other and with how the tests look them up:

1. ADF-t: regenerates the tables from the complete simulation run, 2,000 files per trend with 250,000 draws each. ENH: Fit the ADF t-test critical values to the same simulations as the p-values #1017 used 7,816 of these files and asked for this rerun.
2. ADF-z: processes its simulations the way ENH: Fit the ADF t-test critical values to the same simulations as the p-values #1017 processes ADF-t. As a result, the ADF-z critical values and p-values are consistent, and the critical values use the nobs that PhillipsPerron passes.
3. Lookups: checks that every critical-value lookup passes the nobs its table was fit in, and corrects the one docstring that described it wrongly.

1. ADF-t from the complete run

The output barely changes:

• P-values below 0.15: they change from main's by at most 0.00001.
• Elsewhere: the largest change is 0.0006, with c, where the cut-off moves from -1.72243 to -1.70276. With the other trends, p changes by at most 0.00004.
• Critical values: they change by at most 0.00003.

The p-values of the asymptotic 1%, 5% and 10% critical values are within 0.000012 of 1%, 5% and 10%. In the tail, the largest relative error of p-values at or below 0.15 is at most 0.06% (5.7 standard errors).

2. ADF-z made consistent

adf_z_simlation_process.py now works like adf_t_simulation_process.py:

• Sample size: the columns are labeled nobs = T − 1, the number of observations in the regression. They were labeled with the series length T, but PhillipsPerron (test_type="rho") passes T − 1 to mackinnoncrit. So the critical values were those of a sample one observation shorter, off by up to 0.35 with 25 observations and 0.03 with 100.
• Critical values: they come from estimate_response_surface, which drops the highest power of 1/nobs while it's insignificant and then refits. On main, estimate_cv_regression had set the 1/T³ terms of the 5% and 10% values with n and c to 0 without refitting.
• P-value: it's fit to the asymptotic quantiles, the constants of the regressions, in place of the quantiles with T=2000. The piece below the cut-off is now a quartic in log|stat|, in place of a cubic. fit_smooth_pval_model accepts small_order=5, and its junction and monotonicity code already handled any order.
• Script: the files are sorted, the script takes --data-path, --output and --ex-size, and it prints the errors of the fits.

These are the p-values of the asymptotic 1%, 5% and 10% critical values:

	n	c	ct	ctt
main	0.00991, 0.04980, 0.09966	0.00986, 0.04964, 0.09951	0.00975, 0.04933, 0.09907	0.00966, 0.04906, 0.09866
cubic in log|stat|	0.010003, 0.049999, 0.099924	0.010003, 0.049995, 0.099969	0.010002, 0.049995, 0.099984	0.010000, 0.049999, 0.099991
this PR (quartic)	0.010001, 0.049995, 0.100042	0.010001, 0.049996, 0.100002	0.010001, 0.049995, 0.099999	0.010000, 0.049999, 0.100001

• The p-value fit: the quartic improves the tail for every trend. The largest relative error of p-values at or below 0.15 is at most 0.05% (0.13% with the cubic), against up to 6.0% in 8.0.

  	n	c	ct	ctt
  Largest error, p ≤ 0.15: cubic → quartic	2.0e-4 → 6.9e-5	8.4e-5 → 1.4e-5	4.1e-5 → 1.3e-5	2.0e-5 → 8.1e-6
  Largest error, p > 0.15: cubic → quartic	0.0118 → 0.0133	0.0017 → 0.0015	0.0011 → 0.0006	0.0011 → 0.0003

  The only cost is a slightly larger body error with n. The p-values of the asymptotic critical values are within 0.00005 with n and within 0.000005 otherwise. With n this is still looser than ADF-t (0.00002), because of the large-p cubic.

• The critical-value regressions: they're within 2.6 standard errors of the average simulated quantile at every nobs, except with ctt at nobs = 24, where they're off by up to 0.0075 (7 standard errors at 1%, 4 at 5%). A cubic in 1/nobs doesn't quite follow ctt in the smallest samples.

• Changes from 8.0 with a constant or a trend:

  • Critical values change by up to 0.49 with 19 observations, by at most 0.032 with 100 or more, and by at most 0.002 asymptotically.
  • P-values at or below 0.15 change by at most 0.0015. The largest change is 0.014, at a p-value near 0.7 with c.

• Changes with n: the 1%, 5% and 10% values with 100 observations are -13.09, -7.79 and -5.56. The p-value of -8 is 0.0506.

This part is the work of a separate session (branch wip-adf-z-cv), whose commits are cherry-picked here. The quartic was added afterwards.

3. Lookups

Each table and the nobs that is used to look it up:

Table	Fit in	Looked up with	Consistent
ADF-t (ADF, PhillipsPerron tau)	regression nobs (T − 1)	resols.nobs	yes
ADF-z (PhillipsPerron rho)	series length T	resols.nobs (T − 1)	fixed here
DFGLS	regression nobs (T − 1)	resols.nobs	yes
Engle-Granger	residual ADF regression nobs	resid.shape[0] - lags - 1	yes (docstring corrected)
Phillips-Ouliaris	series length T	z.shape[0] (T)	yes
KPSS, Zivot-Andrews	asymptotic only	—	—

The engle_granger_cv docstring said that nobs is the number of observations in the time series. It's the number of observations in the ADF regression of the residuals, which engle_granger passes.

• Not changed, Engle-Granger: the simulation computes the t statistic with the residual variance divided by n, but engle_granger uses ADF, which divides by n − k. In small samples this makes the critical values a little too far from 0, about 2% of the statistic with 24 observations.
• Not changed, DFGLS: the simulation divides by the regression's nobs, with a # DOF correction? comment in the code. DFGLS divides by nobs − 1.
• Fixing either: it needs new simulations, so it isn't done here.

Checks

• Data: all 8,000 ADF-t files load as 124 × 31 arrays. They are finite and increase with the probability, and no two are identical. So do the 8,000 ADF-z files (2,000 per trend).
• Processing: running adf_z_simlation_process.py and then adf_t_simulation_process.py on this branch reproduces dickey_fuller.py byte for byte.
• Release note: the numbers in the ADF-z note were rechecked against main and 8.0.
• Tests:
  • The unit root tests and test_lower_case_options.py pass (8,300).
  • The full suite passes with --skip-slow (31,582 passed, 812 skipped).
  • The docstring examples of arch.unitroot pass.
  • black, isort, ruff and flake8 pass, mypy finds no new errors, and docutils parses the release notes with no messages.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.44%. Comparing base (67045ff) to head (176e243).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1018   +/-   ##
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  Coverage   99.44%   99.44%           
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  Files         153      153           
  Lines       34259    34278   +19     
  Branches     2594     2595    +1     
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+ Hits        34069    34088   +19     
  Misses        114      114           
  Partials       76       76           

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