Ordinary Least Squares (OLS)

Fit an Ordinary Least Squares (OLS) regression of dependent_ticker on independent_tickers.

Also known as: linear regression, least squares regression.

For more information about the method, see regression_model.get_ols.

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Calculate the Ordinary Least Squares (OLS) in Python

The Ordinary Least Squares (OLS) is available in the Econometrics module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_ols as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(["AMZN", "TSLA"], api_key="FINANCIAL_MODELING_PREP_KEY")

# AMZN (the first ticker) is dependent; TSLA is independent
toolkit.econometrics.get_ols(period="quarterly")

# Or, override which ticker is dependent/independent, and pull in Benchmark too
toolkit.econometrics.get_ols(
    dependent_ticker="AMZN",
    independent_tickers=["TSLA", "Benchmark"],
    period="quarterly",
    cov_type="HC1",
)
# Or, simply opt every default independent ticker (here, just TSLA) into
# including Benchmark too:
toolkit.econometrics.get_ols(period="quarterly", include_benchmark=True)

# Or, use Newey-West (HAC) standard errors for time-series regressions
# where errors may be both heteroskedastic and autocorrelated:
toolkit.econometrics.get_ols(period="quarterly", cov_type="HAC", maxlags=4)

Which returns:

(for the first call, AMZN regressed on TSLA)

Parameters

get_ols accepts the following parameters:

• dependent_ticker (str | None, optional): The dependent (predicted) asset. Defaults to None, meaning the Toolkit instance’s first ticker.
• independent_tickers (str | list[str] | None, optional): The independent (predictor) asset(s). Defaults to None, meaning every other ticker in the Toolkit instance besides dependent_ticker.
• include_benchmark (bool, optional): Whether to include “Benchmark” in the default independent ticker(s) (has no effect when independent_tickers is given explicitly). Defaults to False.
• period (str, optional): The data frequency (daily, weekly, monthly, quarterly, or yearly). Defaults to “daily”.
• column (str, optional): The historical data column to regress on. Defaults to “Return”.
• add_constant (bool, optional): Whether to include an intercept. Defaults to True.
• cov_type (str, optional): Which covariance estimator to use for the standard errors – one of “nonrobust” (classical, assumes homoskedastic errors), “HC0”/”HC1”/”HC2”/”HC3” (heteroskedasticity-robust), “cluster” (cluster-robust, requires clusters) or “HAC” (Newey-West, heteroskedasticity-and-autocorrelation-consistent, requires maxlags). Use get_breusch_pagan_test/get_white_test to check for heteroskedasticity and get_ljung_box_test to check for autocorrelation first. Defaults to “nonrobust”.
• clusters (pd.Series | None, optional): The cluster label for each observation (e.g. a coarser time bucket derived from the return index, to correct for within-period correlation), required when cov_type="cluster". Aligned to the regression’s own index before use, so it may be indexed by the full period index even though the regression drops periods with missing data. Defaults to None.
• maxlags (int | None, optional): The maximum lag to include when estimating the HAC (Newey-West) covariance matrix, required when cov_type="HAC". A common rule of thumb is floor(4 * (n / 100)^(2/9)) (Newey & West, 1994). Defaults to None.
• rounding (int | None, optional): The number of decimals to round the results to. Defaults to None.

Related Regression

The Econometrics module page introduces the module, and the sidebar lists all of its functions.