Novel - pertaining to peak flows, you may be adequate if your record contains the extreme flow estimates of all the paleo-floods.  If your record contains "extreme" events, it is more apt to be adequate when the confidence limits are extended.  

Adequacy is more of an opinion, than a statement of fact.  What parameters signify adequacy?  If the predictions of model are within +/- 50%, 80% of time, is that adequate?  Let's just say you have found a great model, it includes all the important elements.  Your country has a great network of rainfall, streamflow, wells, climactic records, water quality, variety of geologies, soils, stream types, elevations, and land uses on the watersheds.  If your model works satisfactorily for the purposes of its use and yield "adequate results", whereever applied, you should celebrate much success.  Part of the determination of adequacy depends on existing data, statistics and knowledge, and part that may effect lives, property, infrastructure, may well depend on not only what is likely, and what is very infrequent, but also what is possible.  With more availability of information on extreme events, such as the October 3-4, 2015 storm aimed at South Carolina, we begin to realize what is improbable, but possible.  As long as we have a healthy knowledge and view our our model adequacey AND inadequacy, we can qualify and set the boundaries of use and prediction.

I have never heard about a model result that would approve or reject the use of one time series to set hydrometeorological modelling. It is rather a matter of data quality. You should test the quality of your data first, otherwise your modelling would mean nothing, even if you get nice results.

The Hurst exponent does not actually a measure adequacy. It measures the persistancy character of a time series, that is if it shows some behaviour other than random in time.

In any case a hydrological time series is a sample of possible events, thus raising questions about its representativity and the stationarity of the event population being sampled. Since there is no possible way to have a real representative sample (since climate changes), where all possible events are equally (proportionally) likely to being measured, the issue of "adequacy" in these terms will never be trully solved. In reallity, all estimators based on our measurments of hidrological events will be biased.

So if I may add, it is not an issue of adequacy but one of trustability. In this case, there are two necesary conditions to qualify time series trustability: one is the quality of the data itself as Gil Mahe points out. The other one is the time scale and time period for which our results and interpretations are valid, which should be limited to the periods for which we have enough knowledge (for example the measured period).

On a side note, there is for example the "magical" 30 years record period. This criteria is only based on the fact that at a value of n=30, sampling precision becomes large "enought" (standard error becomes low). Again the question of what is "good enought" as William Hansen points out.