Durbin-Watson Test

Calculate the Durbin-Watson statistic for first-order autocorrelation in the residuals of a regression of dependent_ticker on independent_tickers.

OLS standard errors assume that the residuals of consecutive periods are uncorrelated. The Durbin-Watson statistic compares each residual with the one before it.

The formula is as follows:

• e_t are the residuals of the OLS regression of the dependent ticker’s column (Return by default) on the independent tickers’ column

• Interpretation: DW < 1.5 positive autocorrelation likely, DW > 2.5 negative autocorrelation likely, otherwise no strong evidence

The statistic ranges from 0 to 4. A value near 2 means no first-order autocorrelation; values below 2 point to positive autocorrelation (consecutive residuals tend to share the same sign, often a sign of an omitted trend or lagged effect) and values above 2 to negative autocorrelation (residuals tend to alternate in sign). Like heteroskedasticity, autocorrelation leaves the coefficients unbiased but makes the standard errors unreliable; a “HAC” cov_type in get_ols, or get_gls with an AR(1) omega, are common remedies. There is no exact p-value: the returned interpretation is a rule of thumb (below 1.5 is likely positive, above 2.5 likely negative autocorrelation).

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

• Durbin, J., & Watson, G.S. (1950). “Testing for Serial Correlation in Least Squares Regression I.” Biometrika, 37(3/4), 409-428.

Also known as: DW statistic.

Durbin-Watson Test in Python or via the MCP

Install the Finance Toolkit with:

pip install financetoolkit -U

Then call get_durbin_watson_test as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(
    ["HD", "LOW"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2025-01-01",
    end_date="2025-12-31",
)

# HD (the first ticker) is dependent; LOW is independent
toolkit.econometrics.get_durbin_watson_test()

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

Which returns:

Using Your Own Data

get_durbin_watson_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:

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")

econometrics.get_durbin_watson_test()

Parameters

get_durbin_watson_test accepts the following parameters.

Related Diagnostics