45 lines
1.7 KiB
Python
45 lines
1.7 KiB
Python
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import numpy as np
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import pandas as pd
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from scipy.stats import norm
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from btcmodel.forecast import Forecast, crps, pit
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def normal_crps(mu, sigma, y):
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"""Closed-form CRPS of N(mu, sigma^2) at y."""
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z = (y - mu) / sigma
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return sigma * (z * (2 * norm.cdf(z) - 1) + 2 * norm.pdf(z) - 1 / np.sqrt(np.pi))
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def test_crps_matches_closed_form_for_normal():
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f = Forecast.normal("2020-01-01", np.array([1, 2, 3]), mean=[0.0, 1.0, 2.0], sd=[1.0, 0.5, 2.0])
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y = np.array([0.3, -0.2, 5.0])
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expected = normal_crps(np.array([0.0, 1.0, 2.0]), np.array([1.0, 0.5, 2.0]), y)
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np.testing.assert_allclose(crps(f.log_quantiles, y), expected, rtol=0.02)
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def test_crps_prefers_the_right_forecast():
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y = np.array([0.0])
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good = Forecast.normal("2020-01-01", np.array([1]), 0.0, 0.1)
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biased = Forecast.normal("2020-01-01", np.array([1]), 0.5, 0.1)
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vague = Forecast.normal("2020-01-01", np.array([1]), 0.0, 2.0)
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assert crps(good.log_quantiles, y) < crps(biased.log_quantiles, y)
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assert crps(good.log_quantiles, y) < crps(vague.log_quantiles, y)
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def test_pit_and_intervals():
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f = Forecast.normal("2020-01-01", np.array([1, 1, 1]), 0.0, 1.0)
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np.testing.assert_allclose(
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pit(f.log_quantiles, [0.0, 1.0, -10.0]), [0.5, 0.841, 0.0], atol=0.01
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)
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lo, hi = f.interval(0.95)
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np.testing.assert_allclose(hi, 1.96, atol=0.01)
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np.testing.assert_allclose(lo, -1.96, atol=0.01)
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def test_from_samples_recovers_quantiles():
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rng = np.random.default_rng(0)
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f = Forecast.from_samples("2020-01-01", np.array([10]), rng.normal(0, 1, size=(200_000, 1)))
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np.testing.assert_allclose(f.quantile(0.5), 0.0, atol=0.02)
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assert f.dates[0] == pd.Timestamp("2020-01-11")
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