  Complex systems such as protein conformational fluctuations and supercooled
liquids exhibit a long relaxation time and are considered to posses multiple
relaxation times. We analytically obtain the exact correlation function for
stochastic processes with multiple relaxation times. We show that the
time-averaged correlation function calculated by a trajectory whose length is
shorter than the longest relaxation time exhibits an apparent aging behavior.
We propose a method to extract relaxation times from a single trajectory. This
method successfully extracts relaxation times of a stochastic process with
multiple states when a state can be characterized by the values of the
trajectory. As an application of this method, we estimate several relaxation
times smaller than the longest relaxation time in conformational fluctuations
of a small protein.
