  Classical portfolio optimization methods typically determine an optimal
capital allocation through the implicit, yet critical, assumption of
statistical time-invariance. Such models are inadequate for real-world markets
as they employ standard time-averaging based estimators which suffer
significant information loss if the market observables are non-stationary. To
this end, we reformulate the portfolio optimization problem in the spectral
domain to cater for the nonstationarity inherent to asset price movements and,
in this way, allow for optimal capital allocations to be time-varying. Unlike
existing spectral portfolio techniques, the proposed framework employs
augmented complex statistics in order to exploit the interactions between the
real and imaginary parts of the complex spectral variables, which in turn
allows for the modelling of both harmonics and cyclostationarity in the time
domain. The advantages of the proposed framework over traditional methods are
demonstrated through numerical simulations using real-world price data.
