中级计量经济学 第八讲
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Testing for Serial Correlation 检验序列相关
Correcting for Serial Correlation with Strictly Exogenous Regressors 当自变量为严格外生时校正序列相关
Differencing and Serial Correlation 差分和序列相关
This assumption implies that ut is uncorrelated with any of the xkj. 这个假定可推出ut 与任何xkj都不相关。
定理 10.1 (OLS的无偏性):在假定TS.1-3下，OLS估计量 条件于X是无偏的，因此也是无条件无偏。
7
The assumption TS2
假定 TS2
We need to discuss more about TS2. It assumes that E(ut|X)=0, t=1,…,n, where X denotes all the independent variables in all the time periods. 我们需要更多的讨论关于TS2。它假定了E(ut|X)=0, t=1,…,n, 其中X表示所有时期的所有自变量。
分析截面数据时，如果我们把数据按特定方式排序，序列相关的问 题也可能发生，然而由于系统产存在时间上的惰性，它在时间序列 分析中更为常见。
For this reason it is often called autocorrelation.
因为这个原因，它常常被称作是自相关。
4
Basic Regression Analysis with Time Series Data
假定 TS.3：没有完全共线性
Theorem 10.1 (Unbiasedness of OLS): Under Assumptions
TS.1-3, the OLS estimators are unbiased conditional on X,
and therefore unconditionally as well: E bˆj b j, j 1,...,k
时间序列数据的基本回归分析
We focus on discussing the Gauss-Markov assumptions for time series applications. 我们集中讨论时间序列版的高斯-马尔可夫假定。
The Nature of Time Series Data 时间序列数据的本质 A time series data set is a sequence of random variables indexed by time. 时间序列数据是以时间为指标的一个随机变量序列。 Time series data set comes with a temporal ordering. 时间序列数据集伴随着一个时间上的排序。
5
Basic Regression Analysis with Time Series Data
时间序列数据的基本回归分析
Example: a static model
yt b0 b1zt ut , t 1,...,T
例：一个静态模型
yt b0 b1zt ut , t 1,...,T
A dynamic model一个动态模型
yt yt1 xt ut
6
Time Series Data: Finite Sample Properties of OLS Under Classical Assumptions
时间序列数据：在经典假定下OLS的有限样本性质
Unbiasedness of OLS
当误差项协方差不为零时，序列相关就出现了。即，对某些观察值i 和m,
cov(ui,um)˜=0. Even though the problem of serial correlation can also
happen to cross-section data when the data are ordered in a specific way, it is a frequent one when using time series due to inertia in the system.
Heteroskedasticity in Time Series Regression 时间序列回归中的异方差性
2
Lecture Outline
讲义大纲
What is serial correlation 什么是序列相关
Basic introduction of time series analysis 时间序列分析的基本介绍
OLS的无偏性
Assumption TS.1:
Linear in parameters
假定 TS.1: 模型对于参数呈线性关系
Assumption TS.2: 假定 TS.2: 零条件期望
Zero conditional mean
Assumption TS.3:
No perfect collinearity
Multiple Regression Analysis 多元回归分析之序列相关
y = b0 + b1xt1 + b2xt2 + . . . b百度文库xtk + u
Serial Correlation 序列相关
1
Chapter Outline
本章大纲
Properties of OLS with Serially Correlated errors 误差序 列相关时OLS的性质
Properties of OLS with Serially Correlated Errors 误差序列相关时OLS的性质
Testing for Serial Correlation 检验序列相关
3
What is serial correlation
什么是序列相关
Serial correlation happens when the covariances of the error terms are not zero, that is, for some individuals i and m,
Correcting for Serial Correlation with Strictly Exogenous Regressors 当自变量为严格外生时校正序列相关
Differencing and Serial Correlation 差分和序列相关
This assumption implies that ut is uncorrelated with any of the xkj. 这个假定可推出ut 与任何xkj都不相关。
定理 10.1 (OLS的无偏性):在假定TS.1-3下，OLS估计量 条件于X是无偏的，因此也是无条件无偏。
7
The assumption TS2
假定 TS2
We need to discuss more about TS2. It assumes that E(ut|X)=0, t=1,…,n, where X denotes all the independent variables in all the time periods. 我们需要更多的讨论关于TS2。它假定了E(ut|X)=0, t=1,…,n, 其中X表示所有时期的所有自变量。
分析截面数据时，如果我们把数据按特定方式排序，序列相关的问 题也可能发生，然而由于系统产存在时间上的惰性，它在时间序列 分析中更为常见。
For this reason it is often called autocorrelation.
因为这个原因，它常常被称作是自相关。
4
Basic Regression Analysis with Time Series Data
假定 TS.3：没有完全共线性
Theorem 10.1 (Unbiasedness of OLS): Under Assumptions
TS.1-3, the OLS estimators are unbiased conditional on X,
and therefore unconditionally as well: E bˆj b j, j 1,...,k
时间序列数据的基本回归分析
We focus on discussing the Gauss-Markov assumptions for time series applications. 我们集中讨论时间序列版的高斯-马尔可夫假定。
The Nature of Time Series Data 时间序列数据的本质 A time series data set is a sequence of random variables indexed by time. 时间序列数据是以时间为指标的一个随机变量序列。 Time series data set comes with a temporal ordering. 时间序列数据集伴随着一个时间上的排序。
5
Basic Regression Analysis with Time Series Data
时间序列数据的基本回归分析
Example: a static model
yt b0 b1zt ut , t 1,...,T
例：一个静态模型
yt b0 b1zt ut , t 1,...,T
A dynamic model一个动态模型
yt yt1 xt ut
6
Time Series Data: Finite Sample Properties of OLS Under Classical Assumptions
时间序列数据：在经典假定下OLS的有限样本性质
Unbiasedness of OLS
当误差项协方差不为零时，序列相关就出现了。即，对某些观察值i 和m,
cov(ui,um)˜=0. Even though the problem of serial correlation can also
happen to cross-section data when the data are ordered in a specific way, it is a frequent one when using time series due to inertia in the system.
Heteroskedasticity in Time Series Regression 时间序列回归中的异方差性
2
Lecture Outline
讲义大纲
What is serial correlation 什么是序列相关
Basic introduction of time series analysis 时间序列分析的基本介绍
OLS的无偏性
Assumption TS.1:
Linear in parameters
假定 TS.1: 模型对于参数呈线性关系
Assumption TS.2: 假定 TS.2: 零条件期望
Zero conditional mean
Assumption TS.3:
No perfect collinearity
Multiple Regression Analysis 多元回归分析之序列相关
y = b0 + b1xt1 + b2xt2 + . . . b百度文库xtk + u
Serial Correlation 序列相关
1
Chapter Outline
本章大纲
Properties of OLS with Serially Correlated errors 误差序 列相关时OLS的性质
Properties of OLS with Serially Correlated Errors 误差序列相关时OLS的性质
Testing for Serial Correlation 检验序列相关
3
What is serial correlation
什么是序列相关
Serial correlation happens when the covariances of the error terms are not zero, that is, for some individuals i and m,