第10章序列相关性课件.ppt
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1、第10章序列相关性,Serial Correlation/Autocorrelation,第10章序列相关性Serial Correlation/,Main Contents,What is Serial correlation(Autocorrelation)?The consequences of serial correlationHow to detect the serial correlation?Corrections for serial correlation,Main ContentsWhat is Serial co,What is Serial correlation(
2、Autocorrelation)?,The assumption that errors corresponding to different observations are uncorrelated often breaks down in time-series studies.When the error terms from different(usually adjacent)time periods are correlated,we say that the error term is serially correlated.That is,Cov(ui,uj)0,i.e.E(
3、ui,uj)0 for i j.,What is Serial correlation(Au,Patterns of serial correlation,Patterns of serial correlation,Reasons of serial correlation,Inertia or sluggishnessModel specification errors(omitted variables),Reasons of serial correlationI,What is Serial correlation(Autocorrelation)?,In this chapter,
4、we only deal with the problem of first-order serial correlation,in which errors in one time period are correlated directly with errors in the ensuing period.For example,ut=r ut-1+vtSecond-order serial correlation will be ut=r1ut-1+r2ut-2+vt,What is Serial correlation(Au,第10章序列相关性课件,The consequences
5、of serial correlation(Autocorrelation),OLS estimators will be still unbiased and consistent.take the simple regression as an example Y=b0+b1 X+uWe know the OLS estimator of b1 is,The consequences of serial cor,The consequences of serial correlation(Autocorrelation),The R2 and adj-R2 are still consis
6、tent if the time series is stationary(thats r 1).Or else,for non-stationary time series,the R2 and adj-R2 may be invalid.,The consequences of serial cor,The consequences of serial correlation(Autocorrelation),OLS estimators will not be efficient.The variance of OLS estimators will be biased.,The con
7、sequences of serial cor,The consequences of serial correlation(Autocorrelation),t-statistics and F-statistic will be misleading when there are serial correlation in error terms ut.The variance and standard error of the predicted value will be invalid.,The consequences of serial cor,How to detect the
8、 serial correlation?,Time-sequence plotRuns testDurbin-Watson test,How to detect the serial corre,Time sequence plot,Time sequence plot,Example:Real wages and productivity(Example 10-1),Example:Real wages and produc,Runs test,First,get the sign of the residuals,et,for example,(-)(+)(-)(+)(-),that is
9、,there are 9 negative signs,followed by 8 positive signs and so on.The same signs in the parentheses are called a run.Let N is the number of observations,and N1 is the number of positive signs of the residuals,and N2 is the number of negative signs.And k is the number of runs.,Runs testFirst,get the
10、 sign o,Runs test,Swed and Eisenhart give us a table of critical values.H0:the residual e is stochastic,that is,there is no serial correlation.How to test?If the number of run in your model is less than or equal the critical value n1(table A-6a),and larger than or equal to the critical value n2(A-6b
11、),then we can reject the null hypothesis,H0,means there exists serial correlation.,Runs testSwed and Eisenhart gi,Runs test(example),If the signs of the residual is(-)(+)(-)(+)(-)9 8 4 2 3Then,N1=8+2=10,N2=9+4+3=16,N=26,k=5,then the critical value at 5%significance is 8 and 19.So,if the runs in our
12、model 8 or 19,we should reject the null hypothesis H0.The number of runs in our model is 58,so we reject the H0,which mean there is serial correlation in our model.,Runs test(example)If the sign,Durbin-Watson Test,Durbin and Watson put forward an d statistic(DW).In most software,d-value will be prov
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