Is there a statistic test to compare the level of noise & variation between simulated and original time series.

I have created a simulated time series using Monte Carlo technique from an original time series that I had. I would like to know whether the generated time series is a good representative of the original one or not. I am trying to generate a simulated time series to challenge the robustness of my algorithm,but I want to have a metric (Hypothesis test or,...) to make sure the simulated time series somehow shows a similar behavior and it only contains acceptable level of variations. Can I use Pearson's chi-squared test ?