# 杜宾-瓦特森统计量

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

## 杜宾h-统计量

$h=(1-\frac {1} {2} d) \sqrt{\frac {T} {1-T \cdot \hat Var(\hat\beta_1\,)}}$，滞后因变量回归系数的估计方差$\hat Var(\hat\beta_1)$须满足$T \cdot \hat Var(\hat\beta_1)<1 \,$

## 杜宾-瓦特森面板数据检验

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

## 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.