What question did this study set out to answer?

Determine the distribution of the Von Neumann ratio for least-squares estimated regression disturbances to evaluate serial independence.

December 1, 1961Journal of the American Statistical Association

Testing the Independence of Regression Disturbances

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Authors

HTHenri TheilRoskilde University ANA. L. NagarIndian Institute of Space Science and Technology

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Implication

Methodological study demonstrates a beta approximation for the Von Neumann ratio in smooth regressions, indicating practical significance limits for testing error independence.

Key Points

Determine the distribution of the Von Neumann ratio for least-squares estimated regression disturbances to evaluate serial independence.
Approximated the sampling distribution of the Von Neumann ratio using a beta distribution under the assumption that explanatory variables transition smoothly over time.
Calculated 1% and 5% significance limits across sample sizes ranging from 15 to 100 observations and coefficient counts from 2 to 6.
Demonstrated the application of the theoretical distribution through two empirical examples.
Demonstrated that a beta distribution provides a reliable approximation for regression disturbance ratios when time-series regressors behave smoothly.
Established critical cutoff tables at 1% and 5% significance levels for models with 15 to 100 observations and 2 to 6 adjusted parameters.

Cite This Study

Theil et al. (1961) studied this question.

synapsesocial.com/papers/6a1d2ad128423f2ce504d80b https://doi.org/10.1080/01621459.1961.10482126

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Implication

Methodological study demonstrates a beta approximation for the Von Neumann ratio in smooth regressions, indicating practical significance limits for testing error independence.

Testing the Independence of Regression Disturbances

Discussion

Member takes

Implication

Key Points

Cite This Study

Testing the Independence of Regression Disturbances

Discussion

Member takes

Implication

Key Points

Cite This Study

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