  We develop a first-principles simulation method for attosecond time-resolved
photoelectron spectroscopy. This method enables us to directly simulate the
whole experimental processes, including excitation, emission and detection on
equal footing. To examine the performance of the method, we use it to compute
the reconstruction of attosecond beating by interference of two-photon
transitions (RABBITT) experiments of gas-phase Argon. The computed RABBITT
photoionization delay is in very good agreement with recent experimental
results from [Kl\"under et al, Phys. Rev. Lett. 106 143002 (2011)] and
[Gu\'enot et al, Phys. Rev. A 85 053424 (2012)]. This indicates the
significance of a fully-consistent theoretical treatment of the whole
measurement process to properly describe experimental observables in attosecond
photoelectron spectroscopy. The present framework opens the path to unravel the
microscopic processes underlying RABBITT spectra in more complex materials and
nanostructures.
