  The nature of the post-merger remnant of the first binary neutron star
coalescence observed by the Advanced Laser Interferometer Gravitational Wave
Observatory (Advanced LIGO) and Advanced Virgo, GW170817, is unknown. Searches
have been carried out for short ($\lesssim 1$ s), intermediate ($\lesssim 500$
s), and long ($\sim$ days) signals using various algorithms without yielding a
detection. We describe an efficient frequency tracking scheme based on a hidden
Markov model to search for long-duration transient signals from a neutron star
remnant with spin-down time-scale in the range $\sim 10^2$s-$10^4$s. It was one
of the methods used in the search for signals from a long-lived remnant of
GW170817. We validate the method and estimate its sensitivity through
Monte-Carlo simulations on the same data set as used in the GW170817 search. We
describe the search configuration, procedure, and follow-up step by step. The
methodology of the hidden Markov model is described fully to ensure that future
analyses of this kind can be reproduced by an independent party.
