Durbin-Watson Table (Complete Critical Values Lookup Chart)

Positive Autocorrelation

Consecutive residuals have the same sign — a positive residual tends to follow a positive one. This produces d values near 0. Common in economic time series (GDP, prices, sales) where shocks persist over time.

Negative Autocorrelation

Consecutive residuals alternate in sign — a positive residual tends to follow a negative one. This produces d values near 4. Less common than positive autocorrelation, but can occur in alternating supply-demand or inventory data.

No Autocorrelation

Residuals are randomly distributed with no systematic pattern. Successive residuals are independent of each other. d will be close to 2, falling above d_U and below 4 − d_U. OLS inference is valid in this zone.

Macroeconomics: Consumption and GDP

Regressing annual consumption on GDP over 25 years (k = 1, n = 25) with d = 0.72. At α = 0.05, d_L = 1.29. Since 0.72 < 1.29, positive autocorrelation is detected. This is expected: macroeconomic shocks persist across years. Cochrane-Orcutt or first-differencing corrects the problem before inference on the GDP coefficient.

Finance: CAPM Beta Estimation

Regressing weekly stock excess returns on market excess returns (k = 1, n = 52). d = 2.05. At α = 0.05, d_L = 1.53, d_U = 1.63 for n = 52. Since d > d_U, no autocorrelation — OLS gives valid beta estimates and standard errors. This is typical for equity returns at weekly frequency.

Sales Forecasting: Monthly Revenue Model

A retail company regresses monthly revenue on advertising spend and seasonal dummy variables (k = 3, n = 48). d = 1.19. At α = 0.05 with k = 3, n = 48, d_L ≈ 1.40. Since d < d_L, there is positive autocorrelation. The seasonal adjustment is incomplete — adding AR(1) correction or additional seasonal dummies improves the model.

Energy Economics: Demand and Price Model

Regressing monthly electricity demand on temperature and price (k = 2, n = 60). d = 1.58. At α = 0.05, d_L = 1.51, d_U = 1.65. Since d_L < d < d_U, the result is inconclusive. The researcher should apply the Breusch-Godfrey test before drawing conclusions about the autocorrelation structure.

R

Python (statsmodels)

Stata

SPSS

Requires an intercept

The Durbin-Watson table is only valid when the regression model includes a constant term. For no-intercept models, the critical values differ and the standard table should not be used.

First-order autocorrelation only

The test is designed to detect AR(1) structure (correlation between e_t and e_t−1). It may not reliably detect higher-order autocorrelation (e.g., AR(2) or seasonal). Use the Breusch-Godfrey test for those cases.

No lagged dependent variables

If your regression includes y_t−1 as a predictor (autoregressive model), the Durbin-Watson test is biased toward 2, making it unreliable. Use Durbin's h-test or the Breusch-Godfrey test instead.

Inconclusive zone problem

When d falls between d_L and d_U, the test gives no clear answer. This occurs most often in small samples or when k is large relative to n. Additional tests or a larger sample are needed in this situation.

Ordered observations required

The test is only meaningful when observations have a natural order (time series). For cross-sectional data without natural ordering, the Durbin-Watson statistic has no interpretation and should not be used.

When autocorrelation is found

If H₀ is rejected, standard OLS inference is invalid. Common remedies: Cochrane-Orcutt procedure, Prais-Winsten transformation, Newey-West HAC standard errors, adding lagged variables to the model, or first-differencing.

Using d to conclude significance directly

d alone tells you nothing without d_L and d_U. A common error is treating d = 1.60 as "fine" without checking whether it falls above d_U for your specific n and k combination.

Ignoring the inconclusive zone

When d falls between d_L and d_U, the honest answer is "inconclusive." Researchers sometimes incorrectly conclude "no autocorrelation" from an inconclusive result. The appropriate response is to apply the Breusch-Godfrey test or gather more data.

Using the wrong k in the table

k is the number of predictor variables, not counting the intercept. A regression of y on x₁, x₂, and x₃ has k = 3 even though the model has four parameters (β₀, β₁, β₂, β₃).

Applying the test to cross-sectional data

The Durbin-Watson test requires observations to be ordered in time. Running it on cross-sectional data (e.g., household survey data with no natural ordering) produces a meaningless statistic.

Not interpreting d symmetrically

The table is set up for positive autocorrelation. To test for negative autocorrelation, you must compute d* = 4 − d and compare d* against the same d_L and d_U. Forgetting this step misses one entire tail of possible autocorrelation.

What is the difference between d_L and d_U?

d_L (lower bound) is the cutoff below which positive autocorrelation is clearly present. d_U (upper bound) is the cutoff above which no positive autocorrelation is present. Between them is an ambiguous zone where the test cannot give a definitive answer. Both values increase as n increases and as k increases.

Why does the Durbin-Watson table have two bounds instead of one?

The null distribution of d depends on the values of the regressors X, which differ across datasets. Durbin and Watson showed that regardless of X, the true critical value falls between d_L and d_U. The bounds bracket all possible true critical values, producing a conservative but valid test with three possible outcomes rather than two.

Is a Durbin-Watson value of 1.80 acceptable?

Whether d = 1.80 is acceptable depends entirely on n and k. For n = 50 and k = 2, d_U ≈ 1.63, so d = 1.80 > d_U means no autocorrelation. For n = 20 and k = 3, d_U ≈ 1.68, so the same d = 1.80 still clears the threshold. Always check the specific table values — do not rely on rules of thumb alone.

My n is larger than what the table covers. What do I do?

For n > 100, d_L and d_U converge and the inconclusive zone essentially disappears. Statistical software computes exact p-values via numerical approximation for any n. The Imhof procedure or Pan's algorithm, implemented in R's dwtest() and Python's durbin_watson(), handles large samples without needing the table.

What should I do if the Durbin-Watson test is inconclusive?

Apply the Breusch-Godfrey test, which has a standard chi-square distribution under H₀ and avoids the inconclusive zone problem entirely. Alternatively, inspect the residual plot against time visually, increase the sample size if possible, or use Newey-West standard errors as a precaution if autocorrelation cannot be ruled out.

Why Autocorrelation Matters for Regression

When residuals are correlated, OLS coefficient estimates remain unbiased but are no longer efficient. More importantly, the standard errors are wrong — typically underestimated when positive autocorrelation exists. This means t-statistics are inflated and hypothesis tests on individual coefficients give misleading results. The regression assumptions page at Statistics Fundamentals covers the full set of OLS conditions.

Relationship Between d and the Sample Correlation ρ̂

For large samples, d ≈ 2(1 − ρ̂), where ρ̂ is the estimated first-order autocorrelation of residuals. A quick approximation: d = 1.40 implies ρ̂ ≈ 0.30; d = 0.80 implies ρ̂ ≈ 0.60. This relationship helps interpret the magnitude of autocorrelation in practical terms. Compare this to the Pearson correlation table for understanding correlation magnitudes.

Why the Durbin-Watson Test Remains Standard

Despite being published in 1950–1951, the Durbin-Watson test remains standard in econometrics textbooks and software because it is simple, intuitive, and specifically designed for OLS residuals. Its main competitor, the Breusch-Godfrey test, is more flexible but requires software. The Durbin-Watson table works for hand calculations and exam settings where software is unavailable. See the residuals guide for context on regression diagnostics.