fix(arima): keep seasonal period in search_arima fallback (#1276)

[Ajay Mathuriya (ajaycodesitbetter)]

Fixes #1276.

When the non-approximate refit gives infinite ic, search_arima recursed without period, so the fallback search used the default period=1 and returned a non-seasonal model. This passes period=period in that recursive call.

Adds a regression test that forces the fallback and checks that the seasonal period is kept for every model fitted (fails before the fix, passes after). The full tests/test_arima.py passes locally.

Note: the failing path is rare (stepwise=False, approximation=True, exact refit fails). I forced it with a mock in the test.

I used AI assistance to help write and verify this change; I reviewed it myself.

[Copilot]

Copilot was unable to review this pull request because the user who requested the review has reached their quota limit.

[CLAassistant]

All committers have signed the CLA.

[José Morales (jmoralez)]

Thanks for the fix! Could you also add an end-to-end test that goes through auto_arima_f with stepwise=False, so we also cover how the arguments reach search_arima and not only search_arima itself? Something like this fails on main (assert 1 == 12) and passes with your change:

def test_auto_arima_nonstepwise_fallback_keeps_seasonal_period(monkeypatch):
    original = arima_module.myarima
    state = {"failed": False}

    def myarima_refit_fails(*args, **kwargs):
        fit = original(*args, **kwargs)
        if kwargs.get("approximation") is False and not state["failed"]:
            state["failed"] = True
            fit = {**fit, "ic": math.inf}
        return fit

    monkeypatch.setattr(arima_module, "myarima", myarima_refit_fails)
    fit = arima_module.auto_arima_f(
        ap, period=12, stepwise=False, approximation=True, max_order=3
    )
    assert state["failed"]
    assert fit["arma"][4] == 12

[José Morales (jmoralez)]

Thanks for the fix! I left a suggestion to simplify the tests a bit.

[José Morales (jmoralez)]

The two tests repeat the same myarima wrapper, so this moves it into a fixture. It also limits the auto_arima_f grid to order 1 so the end-to-end test runs in ~1.5s instead of ~5s, checks that every model it fits uses period 12, and restores the blank lines before the next test block. Both tests still fail without the period=period fix.

Suggested change

	def test_search_arima_fallback_keeps_seasonal_period(monkeypatch):
	# when the non-approximate refit of the best model has infinite ic,
	# search_arima falls back to a full search that must keep the seasonal period
	rng = np.random.default_rng(0)
	season = 12
	x = np.sin(np.arange(120) * 2 * np.pi / season) + rng.normal(size=120) * 0.3
	original = arima_module.myarima
	state = {"failed": False}
	seen_periods = []
	def myarima_refit_fails(*args, **kwargs):
	seen_periods.append(kwargs["seasonal"]["period"])
	fit = original(*args, **kwargs)
	if kwargs.get("approximation") is False and not state["failed"]:
	state["failed"] = True
	fit = {**fit, "ic": math.inf}
	return fit
	monkeypatch.setattr(arima_module, "myarima", myarima_refit_fails)
	with warnings.catch_warnings():
	warnings.simplefilter("ignore")
	fit = arima_module.search_arima(
	x,
	max_p=1,
	max_q=1,
	max_P=1,
	max_Q=1,
	max_order=3,
	approximation=True,
	offset=0,
	period=season,
	)
	assert state["failed"]
	# every model fitted, including those in the fallback search, uses the period
	assert set(seen_periods) == {season}
	assert fit["arma"][4] == season
	def test_auto_arima_nonstepwise_fallback_keeps_seasonal_period(monkeypatch):
	# end-to-end: the period given to auto_arima_f(stepwise=False) must survive
	# the fallback search that search_arima runs when the exact refit fails
	original = arima_module.myarima
	state = {"failed": False}
	def myarima_refit_fails(*args, **kwargs):
	fit = original(*args, **kwargs)
	if kwargs.get("approximation") is False and not state["failed"]:
	state["failed"] = True
	fit = {**fit, "ic": math.inf}
	return fit
	monkeypatch.setattr(arima_module, "myarima", myarima_refit_fails)
	with warnings.catch_warnings():
	warnings.simplefilter("ignore")
	fit = auto_arima_f(
	ap, period=12, stepwise=False, approximation=True, max_order=3
	)
	assert state["failed"]
	assert fit["arma"][4] == 12
	@pytest.fixture
	def exact_refit_fails(monkeypatch):
	# makes the first non-approximate refit return an infinite ic, which forces
	# search_arima into its fallback search, and records every seasonal period fitted
	original = arima_module.myarima
	state = {"failed": False, "periods": set()}
	def myarima_refit_fails(*args, **kwargs):
	state["periods"].add(kwargs["seasonal"]["period"])
	fit = original(*args, **kwargs)
	if kwargs.get("approximation") is False and not state["failed"]:
	state["failed"] = True
	fit = {**fit, "ic": math.inf}
	return fit
	monkeypatch.setattr(arima_module, "myarima", myarima_refit_fails)
	return state
	def test_search_arima_fallback_keeps_seasonal_period(exact_refit_fails):
	rng = np.random.default_rng(0)
	season = 12
	x = np.sin(np.arange(120) * 2 * np.pi / season) + rng.normal(size=120) * 0.3
	with warnings.catch_warnings():
	warnings.simplefilter("ignore")
	fit = arima_module.search_arima(
	x,
	max_p=1,
	max_q=1,
	max_P=1,
	max_Q=1,
	max_order=3,
	approximation=True,
	offset=0,
	period=season,
	)
	assert exact_refit_fails["failed"]
	assert exact_refit_fails["periods"] == {season}
	assert fit["arma"][4] == season
	def test_auto_arima_nonstepwise_fallback_keeps_seasonal_period(exact_refit_fails):
	with warnings.catch_warnings():
	warnings.simplefilter("ignore")
	fit = auto_arima_f(
	ap,
	period=12,
	stepwise=False,
	approximation=True,
	max_p=1,
	max_q=1,
	max_P=1,
	max_Q=1,
	max_order=3,
	)
	assert exact_refit_fails["failed"]
	assert exact_refit_fails["periods"] == {12}
	assert fit["arma"][4] == 12