By Michael Coval
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Additional info for A Trader On Wall Street: A Short Term Traders Guide
A common way to solve ¯ 2 = 1 − (1 − R2 ) n−1 . the problem is to adjust R2 for degrees of freedom; this gives R n−k ¯ 2 may decrease with the addition of variables with low explanatory The adjusted R power. 1 Hypothesis testing Suppose that we need to test the null hypothesis H0 : βj = βj0 . com 35 Regression Model Financial Econometrics which is asymptotically distributed N (0, 1) under the null hypothesis. With the additional assumption of iid Gaussian error term, βˆj is normally distributed and the t-statistic follows Student’s t distribution with n − k degrees of freedom.
A consistent estimator of the asymptotic variance of the parameters estimator is var βˆ = σ ˆ 2 (X X) . 3). , where Goodness of fit is summarized by the R2 of the regression R2 = 1 − RSS T SS n T SS = i=1 Yi − Y¯ 2 . The coefficient R2 measures the percentage of the variation of the dependent variable Y that is explained by the variation of the regressors X. The usual R2 has the undesirable feature of never decreasing as more variables are added to the regression, even if the extra variables are irrelevant.
The reason for using several tests is that there are many different possible alternatives for the form of heteroscedasticity. All the tests for autocorrelations and heteroscedasticity can be performed through the command line as well. For the Breusch-Godfrey test for serial correlation we should specify the name of the regression equation we need to test and then the command auto(lags) where lags corresponds to the order of autocorrelation being tested. auto(2) will perform the test for second order autocorrelation in the factor model for IBM stock.