A. Time-varying volatility for the unconditional distribution.
B. Time-varying volatility for the conditional distribution.
C. Time-varying means for the unconditional distribution.
D. Time-varying means for the conditional distribution.
The most likely explanation for "fat tails" is that the second moment or volatility is timevarying for the unconditional distribution. For example, this explanation is much more likely given observed changes in volatility in interest rates prior to a much anticipated Federal Reserve announcement. Examining a data sample at different points of time from the full sample could generate fat tails in the unconditional distribution, even if the conditional distributions are normally distributed.