Although 50 years of scientific work has been invested in building retrospective economic time series, their reliability is still debated, a good example being the two competing nineteenth century French GNP series. Instead of trying to bring up some new details to gauge their respective accuracy, we propose a different route, i.e. testing the intrinsic features of these two series, in absolute terms first, then by benchmarking them to a non-retrospective time series. In order to do that, we rely on new mathematical tools--wavelet spectrum analysis--developed in signal processing. This leads to a new approach, which separates the accuracy of a series between amplitude and time variations, and brings nuanced conclusions as to which of the two series tested is the best: indeed, since a trade-off is almost inescapable between the two criterions of accuracy, the statistical quality of one retrospective time series tends to linger either on one side (amplitude level) or the other (time variations). Our study also shows that variance distribution along the time axis is a good proxy for complex retrospective series accuracy.