Spectral analysis of timeseries data

When timeseries data is acquired from a physical system, there is noise in the data. If the signal/noise ratio is small, then one way to increase this ratio is to acquire more recordings of timeseries data. If the experimenter wants to look at the frequency spectrum by averaging the spectra, then phase information will be lost. There are two ways to avoid this loss of phase information:

1) Take a bispectrum of the data

2) Do the following: Pick a frequency, say 800 Hz. For the first timeseries recording, calculate the FFT, and measure the phase at 800 Hz. This phase angle corresponds to a certain amount of time. Truncate that time from the beginning of the recording, and recalculate the FFT. Put the result in a bin. Repeat this process at 800 Hz for all the recordings, adding up the magnitudes into a bin. The net result is a 1D bin. Now rerpeat this entire process for 801 Hz, then for 802 Hz, etc., and then put all the 1D bins side-by-side to create a 2D bin. Plotting this as a 3D surface would show a diagonal feature, and characteristic features above and below the diagonal.

Question: Do both methods yield the same information? Are non-linear features of the timeseries data represented?

-Chris