F-Test

Calculate a nested-model F-test for the joint significance of the regressors in unrestricted_independent_tickers that are not already in restricted_independent_tickers.

Two OLS regressions of dependent_ticker are fitted internally: a “restricted” one on restricted_independent_tickers and an “unrestricted” one that adds the extra tickers. The test checks the null hypothesis that the q extra tickers are jointly zero, i.e. that adding them does not explain the dependent ticker any better, by comparing how much the Residual Sum of Squares (RSS) drops when they are added.

The formula is as follows:

• Both models are OLS regressions of the dependent ticker’s column (Return by default), with a constant when add_constant=True

Where q = k_unrestricted - k_restricted is the number of added regressors, n the number of observations and k_unrestricted the number of parameters of the larger model. Under the null, F follows an F(q, n - k_unrestricted) distribution. A low p-value means the extra tickers meaningfully improve the fit as a group, even when none of them is significant individually. get_likelihood_ratio_test is the asymptotic Maximum Likelihood counterpart.

Also known as: nested F-test, restricted vs. unrestricted F-test, partial F-test.

F-Test in Python or via the MCP

Install the Finance Toolkit with:

pip install financetoolkit -U

Then call get_f_test as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(
    ["AAPL", "MSFT"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2021-01-01",
    end_date="2025-12-31",
)

toolkit.econometrics.get_f_test(
    "AAPL", "MSFT", ["MSFT", "Benchmark"], period="weekly"
)

Or, after setting up the Finance Toolkit MCP, ask:

Which returns:

Using Your Own Data

get_f_test runs on any data, not only prices: ratios, economic indicators, yield curves or your own dataset. Pass a DataFrame, a Series or a dictionary of them to Econometrics as data, with the dates in the rows or the columns, and set changes to how its changes are calculated: "percentage", "log", "difference" for rates and ratios, or None when the data are changes already. For example, for the monthly unemployment rates of the United States and Germany, where each country is a column:

from financetoolkit import Economics, Econometrics

economics = Economics(start_date="2000-01-01")

unemployment = economics.get_unemployment_rate(
    countries=["United States", "Germany"], period="monthly"
)

econometrics = Econometrics(data=unemployment, changes="difference")

Then call econometrics.get_f_test with dependent_ticker, restricted_independent_tickers and unrestricted_independent_tickers, using the column names of the data as tickers.

Parameters

get_f_test accepts the following parameters.

Related Hypothesis Tests