  Motivated by recent advances in the spectral theory of auto-covariance
matrices, we are led to revisit a reformulation of Markowitz' mean-variance
portfolio optimization approach in the time domain. In its simplest incarnation
it applies to a single traded asset and allows to find an optimal trading
strategy which - for a given return - is minimally exposed to market price
fluctuations. The model is initially investigated for a range of synthetic
price processes, taken to be either second order stationary, or to exhibit
second order stationary increments. Attention is paid to consequences of
estimating auto-covariance matrices from small finite samples, and
auto-covariance matrix cleaning strategies to mitigate against these are
investigated. Finally we apply our framework to real world data.
