I have been conducting research in time-series analysis for quite some time and I am familiar with the studies performed within territory of the time domain. However, there are also numerous books and topics which consider the frequency domain. In fact most top papers in statistics which consider stochastic processes seem to show the maths in parts using both the spectral representation and the time-series representation.
What is the reason for this? What information does the spectral representation convey that is not observable in the time-domain? I am trying to convince myself to review books on spectral analysis and as such looking for incentives to do so, as opposed to exploring other topics that are of interest to me.