Hello, I was thinking about the analysis of moments that is usually done to see how well the model explains the data, i.e. when comparing the S.D. of the data with the S.D. of the model, and I see that researchers often claim that the volatility of their model variables is similar to that of the data, but it seems a bit arbitrary to me, what measure or rule of thumb is used to really know or evaluate if two standard deviations are close enough? for example in this case:

Variable | Mean | S.D. data | S.D. Model |
---|---|---|---|

Y | 0.0005 | 0.0183 | 0.0286 |

C | -0.0003 | 0.0179 | 0.0355 |

\Pi_t^c | 1.0103 | 0.0044 | 0.0094 |

\Pi_t | 1.0122 | 0.0081 | 0.0117 |

R_t | 1.0168 | 0.0063 | 0.0094 |

{\rm dS}_t | 1.0108 | 0.0479 | 0.0509 |

Can we say that the model explains well the volatility of the data? Is there a reference measurement?

Greetings to all

Ana