Calculate the Lo-MacKinlay Variance Ratio test for the random walk hypothesis.

The test compares the Variance of q-period (overlapping) compounded returns to q times the Variance of single-period returns. Under the random walk hypothesis these should be equal, giving a Variance Ratio of 1. A Variance Ratio above 1 with a significant (low) p-value indicates positive autocorrelation (momentum/trending behavior), while a Variance Ratio below 1 with a significant p-value indicates negative autocorrelation (mean-reversion).

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

  • Lo, A.W., & MacKinlay, A.C. (1988). “Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test.” Review of Financial Studies, 1(1), 41-66.

Also known as: Lo-MacKinlay test, VR test.

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Calculate the Variance Ratio Test in Python

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

pip install financetoolkit -U

Then call get_variance_ratio_test as shown below.

from financetoolkit import Toolkit

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

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

Which returns:

  AMZN TSLA
Variance Ratio 0.8526 0.7523
Variance Ratio Statistic -0.6757 -1.1353
P-Value 0.4993 0.2563

Parameters

get_variance_ratio_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.
  • q (int, optional): The number of periods to compound returns over. Defaults to 2.
  • 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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