12.1 The Nature of Autocorrelation 1. Definition (1) CLRM assumption: No autocorrelation exist in dishurbances ui; E(iμi)=0 Autocorrelation means: E(μiμ)≠0 (2) Autocorrelation is usually associated with time series data, but it can also occur in cross-sectional data, which is called spatial correlation

One of the CLRM assumptions is: there is no perfect multicollinearity-no exact linear relationships among explanatory variables, Xs, in a multiple regression. In practice, one rarely encounters perfect multicollinearity, but cases of near or very high multicollinearity where explanatory variables are approximately linearly related frequently arise in many applications

The models we discussed are models that are linear in parameters; variables Y and Xs do not necessarily have to be linear The price elasticity of demand~the log-linear models The rate of growth~semilog model Functional forms of regression models which are linear in parameters, but not necessarily linear in variables:

The Object of Hypothesis Testing To answer- How \good\ is the estimated regression line. How can we be sure that the estimated regression function (i.e., the SRF) is in fact a good estimator of the true PRF?

Statistical inference draws conclusions about a population [i.e., probability density function(DF)] from random sample that has supposedly been drawn from that population

2.1 SOME NOTATION 1. The Summation Notation X, =X1++...+n can be abbreviated as:Σx,orΣx 2. Properties of the Summation Operator

在上一章,为了得到投资者的最优投资组合,要求知道: 1、回报率均值向量 2、回报率方差-协方差矩阵 3、无风险利率 估计量和计算量随着证券种类的增加以指数级增加

问题的提出 一、数据背后存在着某种规律性 二、最小二乘保证了3条性质——残差和=0,残差与自变量无关、残差与拟合值无关

1、参数OLS估计的方差增大 2、t检验失效,不能拒绝H0的可能僧大常常犯纳伪错误 3、降低预测

问题的提出 在前述基本假定下OLS估计具有BLUE的优 良性。 然而实际问题中,这些基本假定往往不能 满足,使OLS方法失效不再具有BLUE特性 估计参数时,必须检验基本假定是否满足 ,并针对基本假定不满足的情况,采取相 应的补救措施或者新的方法