Nonstationary Portfolios: Diversification in the Spectral Domain

TL;DR

This paper introduces a spectral domain approach to portfolio optimization that accounts for non-stationarity in asset prices, enabling dynamic, time-varying capital allocations by leveraging complex statistics.

Contribution

It proposes a novel spectral domain framework using augmented complex statistics to model non-stationary market behaviors and improve portfolio diversification.

Findings

Outperforms traditional methods in non-stationary market conditions

Effectively models harmonics and cyclostationarity in asset returns

Demonstrated with real-world price data simulations

Abstract

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.