非平稳投资：谱域中的多样性
Nonstationary Portfolios: Diversification in the Spectral Domain
摘要：
经典的投资组合优化方法通常通过隐含的、但关键的统计时不变假设来确定最优资本分配。这样的模型是不适合现实世界的市场，因为他们采用标准的时间平均为基础的估计，遭受重大的信息损失，如果市场的可观测值是非平稳的。为此，我们重新制定的频谱域中的投资组合优化问题，以满足资产价格变动固有的非平稳性，并以这种方式，允许最佳的资本配置是随时间变化的。与现有的频谱组合技术不同，所提出的框架采用增强的复统计，以利用复频谱变量的实部和虚部之间的相互作用，这反过来又允许在时域中的谐波和循环平稳性建模。所提出的框架比传统的方法的优势，通过使用真实世界的价格数据的数值模拟证明。
英文摘要：
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.
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