Testing CAPM

For better clarity in the results, the number of replications was set to 1500. The bias and the accuracy of the significance tests are provided below for each observation value.
From the above results, the bias for the YSeries is -0.331 and has a very low standard deviation of 0.008. The RMSE (Root Mean Square Error) is an absolute measure of the residuals. A low value indicates a better fit. The RMSE is relatively higher for the Intercept in comparison to the RMSE values for the XSeries and YSeries, suggesting that the latter two parameters exhibit a better absolute fit to the given data. The EDFs from the analysis is shown below:
Based on the above results, X5% should be 1.96 for the null hypothesis to be true. However, the upper tail quantiles in the case of both variables (XSeries and YSeries(-1)) lead to the rejection of the null hypothesis since their 5% values exceed the critical value of 1.96.
The null hypothesis in the case of both the variables is that H0: µ = µ0 for a given value µ0 (sample mean). The alternative hypothesis in either case states that Ha: µ ≠ µ0, indicating a two tailed test.
The power indicates the probability of rejecting the null hypothesis when the true mean differs from the hypothetical mean. From the above two cases, the power for YSeries(-1) is much greater than that for the XSeries indicating a greater probability for rejection of the null hypothesis in the case of the latter.
The figure below shows the bias for the parameters when configured for 30 observations. It appears that the bias has reduced in the case of both estimators as a result of this increase in the number of observations (compared to the earlier simulation with 10 observations) indicating that the new estimates provide a better fit. The RMSE values have also reduced suggesting a similar conclusion. However, the higher RMSE value for the intercept indicates a comparatively lower fit with respect