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2. You are contemplating using the bootstrap to generate new dependent variable data for a regression model by re-sampling from the OLS fitting errors. Your
2. You are contemplating using the bootstrap to generate new dependent variable data for a regression model by re-sampling from the OLS fitting errors. Your model specification is: where the Stata names for these variables are "y" and "x", respectively. (Without the quote marks, of course. You have included in the model enough lags in Y none, in this case) and enough lags in x, (one, in this case) so that the sample autocorrelations in the model fitting errors appear to be serially uncorrelated-which is to say, not linearly related to their own past. Consequently, you are willing to make the assumption required by both the ordinary and the wild bootstrap that the model errors (Ut are serially independent. (Recall that serial independence is a stronger assumption that serial uncorrelatedness: it is assuming that the errors are not related to their own past in any way- linearly or nonlinearly.) You can assume that the delimiter ending each command line is a semicolon. a. State the Stata commands needed in order to estimate the parameters a and B using OLS over observations 12 through 100. (Don't forget the steps you need to take in order for Stata to recognize its "lagging" operator. b. State the commands needed in order to store only the OLS fitting errors under the name "rez hk4" (without the quote marks, of course), and to store only the prediction errors (without 2. You are contemplating using the bootstrap to generate new dependent variable data for a regression model by re-sampling from the OLS fitting errors. Your model specification is: where the Stata names for these variables are "y" and "x", respectively. (Without the quote marks, of course. You have included in the model enough lags in Y none, in this case) and enough lags in x, (one, in this case) so that the sample autocorrelations in the model fitting errors appear to be serially uncorrelated-which is to say, not linearly related to their own past. Consequently, you are willing to make the assumption required by both the ordinary and the wild bootstrap that the model errors (Ut are serially independent. (Recall that serial independence is a stronger assumption that serial uncorrelatedness: it is assuming that the errors are not related to their own past in any way- linearly or nonlinearly.) You can assume that the delimiter ending each command line is a semicolon. a. State the Stata commands needed in order to estimate the parameters a and B using OLS over observations 12 through 100. (Don't forget the steps you need to take in order for Stata to recognize its "lagging" operator. b. State the commands needed in order to store only the OLS fitting errors under the name "rez hk4" (without the quote marks, of course), and to store only the prediction errors (without
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