import numpy as np
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import pytest
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from pandas import (
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DataFrame,
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Series,
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concat,
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)
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import pandas._testing as tm
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def create_mock_weights(obj, com, adjust, ignore_na):
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if isinstance(obj, DataFrame):
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if not len(obj.columns):
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return DataFrame(index=obj.index, columns=obj.columns)
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w = concat(
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[
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create_mock_series_weights(
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obj.iloc[:, i], com=com, adjust=adjust, ignore_na=ignore_na
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)
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for i in range(len(obj.columns))
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],
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axis=1,
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)
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w.index = obj.index
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w.columns = obj.columns
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return w
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else:
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return create_mock_series_weights(obj, com, adjust, ignore_na)
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def create_mock_series_weights(s, com, adjust, ignore_na):
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w = Series(np.nan, index=s.index, name=s.name)
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alpha = 1.0 / (1.0 + com)
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if adjust:
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count = 0
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for i in range(len(s)):
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if s.iat[i] == s.iat[i]:
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w.iat[i] = pow(1.0 / (1.0 - alpha), count)
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count += 1
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elif not ignore_na:
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count += 1
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else:
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sum_wts = 0.0
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prev_i = -1
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count = 0
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for i in range(len(s)):
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if s.iat[i] == s.iat[i]:
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if prev_i == -1:
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w.iat[i] = 1.0
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else:
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w.iat[i] = alpha * sum_wts / pow(1.0 - alpha, count - prev_i)
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sum_wts += w.iat[i]
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prev_i = count
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count += 1
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elif not ignore_na:
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count += 1
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return w
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def test_ewm_consistency_mean(all_data, adjust, ignore_na, min_periods):
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com = 3.0
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result = all_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).mean()
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weights = create_mock_weights(all_data, com=com, adjust=adjust, ignore_na=ignore_na)
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expected = (
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all_data.multiply(weights)
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.cumsum()
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.divide(weights.cumsum())
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.fillna(method="ffill")
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)
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expected[
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all_data.expanding().count() < (max(min_periods, 1) if min_periods else 1)
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] = np.nan
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tm.assert_equal(result, expected.astype("float64"))
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def test_ewm_consistency_consistent(consistent_data, adjust, ignore_na, min_periods):
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com = 3.0
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count_x = consistent_data.expanding().count()
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mean_x = consistent_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).mean()
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# check that correlation of a series with itself is either 1 or NaN
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corr_x_x = consistent_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).corr(consistent_data)
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exp = (
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consistent_data.max()
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if isinstance(consistent_data, Series)
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else consistent_data.max().max()
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)
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# check mean of constant series
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expected = consistent_data * np.nan
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expected[count_x >= max(min_periods, 1)] = exp
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tm.assert_equal(mean_x, expected)
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# check correlation of constant series with itself is NaN
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expected[:] = np.nan
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tm.assert_equal(corr_x_x, expected)
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def test_ewm_consistency_var_debiasing_factors(
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all_data, adjust, ignore_na, min_periods
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):
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com = 3.0
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# check variance debiasing factors
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var_unbiased_x = all_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).var(bias=False)
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var_biased_x = all_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).var(bias=True)
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weights = create_mock_weights(all_data, com=com, adjust=adjust, ignore_na=ignore_na)
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cum_sum = weights.cumsum().fillna(method="ffill")
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cum_sum_sq = (weights * weights).cumsum().fillna(method="ffill")
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numerator = cum_sum * cum_sum
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denominator = numerator - cum_sum_sq
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denominator[denominator <= 0.0] = np.nan
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var_debiasing_factors_x = numerator / denominator
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tm.assert_equal(var_unbiased_x, var_biased_x * var_debiasing_factors_x)
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@pytest.mark.parametrize("bias", [True, False])
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def test_moments_consistency_var(all_data, adjust, ignore_na, min_periods, bias):
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com = 3.0
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mean_x = all_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).mean()
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var_x = all_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).var(bias=bias)
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assert not (var_x < 0).any().any()
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if bias:
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# check that biased var(x) == mean(x^2) - mean(x)^2
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mean_x2 = (
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(all_data * all_data)
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.ewm(com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na)
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.mean()
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)
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tm.assert_equal(var_x, mean_x2 - (mean_x * mean_x))
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@pytest.mark.parametrize("bias", [True, False])
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def test_moments_consistency_var_constant(
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consistent_data, adjust, ignore_na, min_periods, bias
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):
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com = 3.0
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count_x = consistent_data.expanding(min_periods=min_periods).count()
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var_x = consistent_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).var(bias=bias)
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# check that variance of constant series is identically 0
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assert not (var_x > 0).any().any()
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expected = consistent_data * np.nan
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expected[count_x >= max(min_periods, 1)] = 0.0
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if not bias:
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expected[count_x < 2] = np.nan
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tm.assert_equal(var_x, expected)
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@pytest.mark.parametrize("bias", [True, False])
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def test_ewm_consistency_std(all_data, adjust, ignore_na, min_periods, bias):
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com = 3.0
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var_x = all_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).var(bias=bias)
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assert not (var_x < 0).any().any()
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std_x = all_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).std(bias=bias)
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assert not (std_x < 0).any().any()
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# check that var(x) == std(x)^2
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tm.assert_equal(var_x, std_x * std_x)
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cov_x_x = all_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).cov(all_data, bias=bias)
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assert not (cov_x_x < 0).any().any()
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# check that var(x) == cov(x, x)
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tm.assert_equal(var_x, cov_x_x)
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@pytest.mark.parametrize("bias", [True, False])
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def test_ewm_consistency_series_cov_corr(
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series_data, adjust, ignore_na, min_periods, bias
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):
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com = 3.0
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var_x_plus_y = (
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(series_data + series_data)
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.ewm(com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na)
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.var(bias=bias)
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)
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var_x = series_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).var(bias=bias)
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var_y = series_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).var(bias=bias)
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cov_x_y = series_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).cov(series_data, bias=bias)
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# check that cov(x, y) == (var(x+y) - var(x) -
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# var(y)) / 2
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tm.assert_equal(cov_x_y, 0.5 * (var_x_plus_y - var_x - var_y))
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# check that corr(x, y) == cov(x, y) / (std(x) *
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# std(y))
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corr_x_y = series_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).corr(series_data)
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std_x = series_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).std(bias=bias)
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std_y = series_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).std(bias=bias)
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tm.assert_equal(corr_x_y, cov_x_y / (std_x * std_y))
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if bias:
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# check that biased cov(x, y) == mean(x*y) -
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# mean(x)*mean(y)
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mean_x = series_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).mean()
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mean_y = series_data.ewm(
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com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na
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).mean()
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mean_x_times_y = (
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(series_data * series_data)
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.ewm(com=com, min_periods=min_periods, adjust=adjust, ignore_na=ignore_na)
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.mean()
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)
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tm.assert_equal(cov_x_y, mean_x_times_y - (mean_x * mean_y))
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