I need to implement a bootstrap procedure to correctly estimate the coefficients of a regression that is subject to small-sample bias. The regression is: Y = a + bX + e The series of Ys contains annual data.
Following the procedure described in Eleswarapu and Reinganum (Journal of Business, Apr. 2004), I need to estimate an AR(1) of the independent variable X, save the residuals and the estimates of the coefficients. Then I need to randomize, with replacement, the series of residuals. I can then create a series of pseudo-X, using the randomized series of residuals along with the coefficients estimated in the AR(1). The starting values for X(-1) are randomly chosen from the actual data.
On the other hand, I also need to randomize a series of monthly Ys, with replacement, and compute a series of pseudo-Y, which are annual, from the monthly randomized Ys.
Finally, I need to bootstrap the regression Pseudo-Y = a + bPseudo-X + e. This last procedure I know how to implement. It is the creation of the randomized series of residuals, the pseudo-X and pseudo-Y that I haven't been able to do.
Thank you for your attention.
Best regards,
Raquel Oliveira.
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