CUSUM Test

Calculate the CUSUM test for the stability of the mean of returns over time.

The test fits a constant-mean model to the returns and cumulates the (scaled) OLS residuals into a path that behaves like a Brownian Bridge under the null hypothesis of a stable mean. A stable mean keeps the path close to zero, while a mean shift partway through the series (a structural break, e.g. a regime change) drags the path away from zero; the test statistic is the maximum absolute value of that path.

For more information about the method, see the following paper:

• Ploberger, W., & Kramer, W. (1992). “The CUSUM Test with OLS Residuals.” Econometrica, 60(2), 271-285.

Also known as: CUSUM test, CUSUM of OLS residuals test, Ploberger-Kramer test.

CUSUM Test in Python

get_cusum_test is part of the Econometrics module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_cusum_test as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(
    ["AAPL", "MSFT"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2019-01-01",
    end_date="2023-12-31",
)

toolkit.econometrics.get_cusum_test(period="quarterly", within_period=False)

Parameters

get_cusum_test accepts the following parameters:

• period (str, optional): The data frequency for returns (daily, weekly, monthly, quarterly, or yearly). Defaults to “daily”.
• within_period (bool, optional): Whether to calculate the test within the specified period or for the entire period. Thus whether to look at the test within a specific year (if period = ‘yearly’) or look at the entirety of all years. Defaults to False.
• include_benchmark (bool, optional): Whether to include “Benchmark” among the assets tested. Defaults to False.
• rounding (int | None, optional): The number of decimals to round the results to. Defaults to None.

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