Calculate Engle’s Lagrange Multiplier (LM) test for ARCH effects.

The test regresses squared, mean-demeaned returns on lags of themselves and tests whether the resulting R-squared is significantly different from zero. A significant result (low p-value) indicates that the return series exhibits volatility clustering, and a GARCH-family model is an appropriate choice for it. A high p-value suggests fitting GARCH would not be meaningful, since there is no detectable time-varying volatility to model.

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

  • Engle, R.F. (1982). “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica, 50(4), 987-1008.

Also known as: ARCH-LM test, Engle’s ARCH test.

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Calculate the ARCH-LM Test in Python

The ARCH-LM Test is available in the Econometrics module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_arch_lm_test as shown below.

from financetoolkit import Toolkit

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

toolkit.econometrics.get_arch_lm_test(period="quarterly")

Which returns:

  AMZN TSLA
ARCH-LM Statistic 4.0116 3.7793
P-Value 0.548 0.5817

Parameters

get_arch_lm_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.
  • lags (int, optional): The number of lags to test for ARCH effects. Defaults to 5.
  • 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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The Econometrics module page introduces the module, and the sidebar lists all of its functions.

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