A Spectral Generalisation of the Variance Ratio: Eigenstructure of Long-Horizon Portfolio Covariance and a Multi-Memory Factor Model of U.S. Equity Returns
创建于 更新于
摘要
We propose a multivariate, eigenstructure-indexed generalisation of the Lo–MacKinlay variance-ratio, decomposing long-horizon equity-return dynamics into parallel return-channel and volatility-channel memory components. The framework yields a parsimonious five-factor multi-memory model—comprising persistent and antipersistent fractional Brownian factors, an ARFIMA component, a Markov-switching multifractal (MSM) volatility cascade, and a transitory volatility-of-volatility factor—that fits four U.S. panel and a Europe cross-section while recovering seven stylised facts of long-horizon dynamics across all panels. A rolling-window analysis locates a late-1980s regime transition in market-mode volatility, while a cross-channel β-inversion test falsifies a single shared cross-asset loading driving both linear memory and volatility cascade. The results imply that cross-sectional eigenstructure and horizon-dependent variance decomposition encode universal multi-memory structure, with distinct channels carrying return- and volatility-dynamics and with regime shifts that matter for risk and pricing. [page::1]
