第5讲自相关与异方差要点.ppt

未知异方差下的估计：猜测4 2-* 猜测4: 处理： Estimate the regression with OLS. Regress Divide every variable by: Apply OLS to the transformed data. 未知异方差下的估计：变换5 2-* 猜测1:未知 处理：变量取对数 未知异方差下的估计：另一条思路 2-* 思路:仍然用OLS无偏估计 处理：重新正确估计方差，white稳健方差 未知异方差下的估计：另一条思路 2-* 思路:仍然用OLS无偏估计 处理：重新正确估计方差，white稳健方差 此时OLS仍然不是BLUE,但无偏， 多元回归DGP：高斯马尔科夫假定4 4b无自相关假定 含义： 4b任意两个观察的扰动不相关 4c随机抽样可以保证 2-* 自相关 2-* 自相关下的OLS1：OLS无偏性保持 在假定1（线性）、2（满秩）、3（外生）的条件下，OLS估计量无偏 2-* 自相关下的OLS2：不是最小方差 高斯马尔科夫定理（四个假定都用上），OLS估计量是方差最小（最优）的线性无偏估计量BLUE。异方差下： 2-* 自相关下的OLS后果3：t检验，F检验失效 2-* 由于OLS计算的方差不正确，t检验和F检验不再有效 为什么出现自相关 滞后性 遗漏变量 模型形式不正确 自回归 差分 2-* 自相关下OLS的方差 2-* 自相关下GLS 假设AR(1) 2-* 识别自相关：1绘图 绘制残差对时间关系图 绘制残差与残差滞后图 2-* 识别自相关：2Durbin-Watson检验 2-* 14-* Durbin–Watson Test (cont.) In large samples, we can divide the numerator by (T-k-2) and the denominator by (T-k-1) without creating much of a bias. 14-* Durbin–Watson Test (cont.) In large samples, all approximate s2, an estimate of the variance of the error term. 14-* Durbin–Watson Test (cont.) In large samples, approximately estimates the covariance between adjacent error terms. If there is no first-order serial correlation, this term will collapse to 0. 14-* Durbin–Watson Test (cont.) In large sample, the Durbin–Watson statistic approximates Under the null hypothesis of no first-order serial correlation, d ≈ 2 14-* Durbin–Watson Test (cont.) When the Durbin–Watson statistic, d, gives a value far from 2, then it suggests the covariance term is not 0 after all i.e., a value of d far from 2 suggests the presence of first-order serial correlation At the most extreme, Cov(et ,et-1) is bounded by –s?2 and s?2 d is bounded between 0 and 4 自相关检验：通用方法Breusch-Godfrey (BG) test 1、OLS回归获得残差 2、残差对所有x，以及残差滞后（直到滞后p）回归，获得R平方 3、原假设：无自相关。 (n-p)R平方 服从自由度为p的卡方分布 2-* 自相关校正：运用OLS，校正方差 2-* 14-* Newey–West E.S.E.’s (cont.) The first step in estimating Newey–West Standard Errors is to choose a lag, L Then we assume s|t-t’| ≈ 0 for all |t-t’| L The choice of L is a