Suppose I would like to use a method for data prediction, and that I have some empirical data (i.e., sequence of samples of the form [time, value]). Would it be possible to know in advance, based on the data only, if it makes sense to use a model for prediction (based on the samples, used as a training set). 

I am asking this for the following simple reason: it is possible that the sample data is totally random and that there is no correlation at all between the samples. Hence, I would like to avoid trying to find correlations where there is not.