# 杜宾-瓦特森统计量

ett 时段的残差，那么检验的统计量为：${\displaystyle d={\sum _{t=2}^{T}(e_{t}-e_{t-1})^{2} \over {\sum _{t=1}^{T}e_{t}^{2}}}}$

• 如果d <= dL,α ，误差项自相关为正
• 如果d >= dU,α ，不拒绝，无自相关
• 如果dL,α < d < dU,α ，则检验结果无法确认

• 如果(4 - d) <= dL,α ，误差项自相关为负
• 如果(4 - d) >= dU,α ，不拒绝，无自相关
• 如果dL,α < (4 - d) < dU,α ，则检验结果无法确认

## 杜宾h-统计量

${\displaystyle h=(1-{\frac {1}{2}}d){\sqrt {\frac {T}{1-T\cdot {\hat {V}}ar({\hat {\beta }}_{1}\,)}}}}$，滞后因变量回归系数的估计方差${\displaystyle {\hat {V}}ar({\hat {\beta }}_{1})}$须满足${\displaystyle T\cdot {\hat {V}}ar({\hat {\beta }}_{1})<1\,}$

## 杜宾-瓦特森面板数据检验

${\displaystyle d_{pd}={\frac {\sum _{i=1}^{N}\sum _{t=2}^{T}(e_{i,t}-e_{i,t-1})^{2}}{\sum _{i=1}^{N}\sum _{t=1}^{T}e_{i,t}^{2}}}}$

## 参考

• Durbin, J., and Watson, G. S., "Testing for Serial Correlation in Least Squares Regression, I." Biometrika 37 (1950): 409-428.
• Durbin, J., and Watson, G. S., "Testing for Serial Correlation in Least Squares Regression, II." Biometrika 38 (1951): 159-179.
• Gujarati, Damodar N. (1995): Basic Econometrics, 3. ed., New York et al.: McGraw-Hill, 1995, page 605f.
• Verbeek, Marno (2004): A Guide to Modern Econometrics, 2. ed., Chichester: John Wiley & Sons, 2004, Seite 102f.
• Bhargava, A./Franzini, L./Narendranathan, W. (1982): Serial Correlation and the Fixed Effects Models, in: Review of Economic Studies, Vol. 49 Iss. 158, 1982, page 533-549.