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I am testing a stochastic model that generates synthetic hydrologic time series (five-year series, 60(month) data points). I want to evaluate whether these synthetic time series have the same probabilities as the historical series. For this, I'm thinking to use the t-Test with The null hypothesis: the average of 150 synthetic values of each month in each year is statistically equal to the historical mean for the corresponding month.

Is it correct to use this hypothesis testing? if this correct this situation is a two-sample or one sample t test?

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    $\begingroup$ If you have a simulated time series and an actual series and you would like to show that they are realizations of the same stochastic process you would want to look at more properties than just the mean. So a simple t test would not be appropriate. Even if you are only considering the mean the t test us based on independent observations whereas time series data are likely to be autocorrelated. $\endgroup$
    – Michael R. Chernick
    Jul 21, 2017 at 6:36

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