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* PyDocstyle Compliant batch 1 * Batch 2 * Batch 3 * Batch 4 * Batch 5 * Batch 6 * Batch 7 * Linting * MyPy * mypy things * black * more mypy * black * fix that * black again * undo that * Fix error message * pylint --------- Co-authored-by: montezdesousa <79287829+montezdesousa@users.noreply.github.com> Co-authored-by: Danglewood <85772166+deeleeramone@users.noreply.github.com>
110 lines
4.0 KiB
Python
110 lines
4.0 KiB
Python
"""Utility functions for the econometrics extension of the OpenBB platform."""
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import warnings
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from typing import Tuple
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import numpy as np
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import pandas as pd
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import statsmodels.api as sm
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from statsmodels.tsa.stattools import adfuller
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def get_engle_granger_two_step_cointegration_test(
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dependent_series: pd.Series, independent_series: pd.Series
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) -> Tuple[float, float, float, pd.Series, float, float]:
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"""Estimate long-run and short-run cointegration relationship for series y and x.
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Then apply the two-step Engle & Granger test for cointegration.
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Uses a 2-step process to first estimate coefficients for the long-run relationship
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y_t = c + gamma * x_t + z_t
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and then the short-term relationship,
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y_t - y_(t-1) = alpha * z_(t-1) + epsilon_t,
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with z the found residuals of the first equation.
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Then tests cointegration by Dickey-Fuller phi=1 vs phi < 1 in
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z_t = phi * z_(t-1) + eta_t
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If this implies phi < 1, the z series is stationary is concluded to be
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stationary, and thus the series y and x are concluded to be cointegrated.
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Parameters
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----------
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dependent_series : pd.Series
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The first time series of the pair to analyse.
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independent_series : pd.Series
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The second time series of the pair to analyse.
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Returns
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-------
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Tuple[float, float, float, pd.Series, float, float]
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c : float
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The constant term in the long-run relationship y_t = c + gamma * x_t + z_t. This
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describes the static shift of y with respect to gamma * x.
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gamma : float
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The gamma term in the long-run relationship y_t = c + gamma * x_t + z_t. This
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describes the ratio between the const-shifted y and x.
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alpha : float
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The alpha term in the short-run relationship y_t - y_(t-1) = alpha * z_(t-1) + epsilon. This
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gives an indication of the strength of the error correction toward the long-run mean.
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z : pd.Series
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Series of residuals z_t from the long-run relationship y_t = c + gamma * x_t + z_t, representing
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the value of the error correction term.
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dfstat : float
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The Dickey Fuller test-statistic for phi = 1 vs phi < 1 in the second equation. A more
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negative value implies the existence of stronger cointegration.
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pvalue : float
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The p-value corresponding to the Dickey Fuller test-statistic. A lower value implies
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stronger rejection of no-cointegration, thus stronger evidence of cointegration.
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"""
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warnings.simplefilter(action="ignore", category=FutureWarning)
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long_run_ols = sm.OLS(dependent_series, sm.add_constant(independent_series))
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warnings.simplefilter(action="default", category=FutureWarning)
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long_run_ols_fit = long_run_ols.fit()
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c, gamma = long_run_ols_fit.params
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z = long_run_ols_fit.resid
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short_run_ols = sm.OLS(dependent_series.diff().iloc[1:], (z.shift().iloc[1:]))
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short_run_ols_fit = short_run_ols.fit()
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alpha = short_run_ols_fit.params[0]
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# NOTE: The p-value returned by the adfuller function assumes we do not estimate z
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# first, but test stationarity of an unestimated series directly. This assumption
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# should have limited effect for high N, however. Critical values taking this into
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# account more accurately are provided in e.g. McKinnon (1990) and Engle & Yoo (1987).
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adfstat, pvalue, _, _, _ = adfuller(z, maxlag=1, autolag=None)
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return c, gamma, alpha, z, adfstat, pvalue
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def mock_multi_index_data():
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"""Create a mock multi-index dataframe for testing purposes."""
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arrays = [
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["individual_" + str(i) for i in range(1, 11) for _ in range(5)],
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list(range(1, 6)) * 10,
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]
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index = pd.MultiIndex.from_arrays(arrays, names=("individual", "time"))
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df = pd.DataFrame(
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{
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"income": np.random.randint(20000, 80000, size=50),
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"age": np.random.randint(25, 60, size=50),
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"education": np.random.randint(12, 21, size=50),
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},
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index=index,
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)
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return df
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