ECON301_Handout_13_1213_02

# 2 1 18566 ln ln44 sic 18566 3 1 pc for aic 148 158

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(2 1) 185.66 ln ln(44) 1.70 44 44 SIC 185.66 3 1 4.84 41 44 PC For AIC, 1.48 < 1.58, for SC, 1.64 < 1.70, and for PC, 4.38<4.84. So they provide evidence that model (1) is preferable to model (2). 4. Testing for Normality of the Disturbances The normality of disturbances is necessary if the t test, F test, chi- square test etc., are to be valid in small samples 2 . It is therefore a vital part of the specification of the classical model, and should always be tested (Thomas, 1997, p.343). The Jarque-Berra (1980) statistic to test for normality of the disturbances is defined as: 2 Recall that for large samples, the tests will be asymptotically valid even if the disturbances are not normally distributed. How large does the sample size have to be for estimators to display their asymptotic properties? We generally accept that at least it must be larger than 30 but it may not suffice. Goldfeld and Quandt (1972, p.277) report an example in which a sample size of 30 is sufficiently large and an example in which a sample of 200 is required. They also note that large sample sizes are needed if interest focuses on estimation of estimator variances rather than on estimation of coefficients (Kennedy, 2001, p.29).

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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: Lecture Notes 14 2 2 3 4 2 3 2 ( / 3) 6 24 JB T where 2 1 2 ˆ T t t u T , 3 1 3 ˆ T t t u T and 4 1 4 ˆ T t t u T (second, third and fourth moments of the residuals about their zero mean). It is possible to show that, under the null hypothesis of normally distributed disturbances, the JB test statistic has a chi-square distribution with 2 degrees of freedom: 2 2 ( ) df JB We therefore reject the null hypothesis of normality if JB exceeds the relevant critical chi-square value: 2 2 ( ) df JB The Jarque-Bera test for normality is also sometimes regarded as a test of misspecification. It is useful for detecting what are known as “outliers” among the data observations. An outli er refers to an observation with a very large residual, that is, a case where the fitted value of the dependent variable is very different from the actual one (Thomas, 1997, p.346)
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