We do comparison of the new valuation model with or without volatility, for nominal or real version of earnings. We discuss which has the best innovations, according to the L1 norm of the autocorrelation function. We consider various averaging windows from 1 to 10.
Methodology: We reject the model if one of two of these norms, for original and absolute values of innovations, is greater than 0.63. W (white noise) = fail to reject. And G = Gaussian, F (fat tails) = not Gaussian (at least one of two Shapiro-Wilk and Jarque-Bera tests gives us 
| Vol? | Infl? | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| No | Nom | W F | W G | W G | W F | Reject | Reject | Reject | Reject | W F | W F |
| No | Real | W F | W G | W G | W G | W G | W G | W G | W G | W G | W F |
| Yes | Nom | W G | W G | W G | Reject | Reject | Reject | Reject | Reject | Reject | Reject |
| Yes | Real | W G | W G | W G | W G | W G | W G | W G | Reject | Reject | Reject |
| Vol? | Infl? | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| No | Nom | 17 | 12 | 11 | 10 | 10 | 10 | 10 | 9 | 9 | 10 |
| No | Real | 17 | 12 | 11 | 10 | 9 | 9 | 9 | 9 | 9 | 9 |
| Yes | Nom | 21 | 21 | 22 | 24 | 26 | 26 | 27 | 27 | 27 | 29 |
| Yes | Real | 21 | 21 | 22 | 23 | 25 | 24 | 25 | 25 | 25 | 26 |
Conclusion: The best model for real version is with volatility, lags 5-7. The best model for nominal version is with
See the GitHub repository file bubble-selection.py and the data file century.xlsx.
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