Conditional spectral methods

We model predictive scale-specific cycles. By employing suitable matrix representations, we express the forecast errors of covariance-stationary multivariate time series in terms of conditionally orthonormal scale-specific bases. The representations yield conditionally orthogonal decompositions of these forecast errors. They also provide decompositions of their variances and betas in terms of scale-specific variances and betas capturing predictive variability and co-variability over cycles of alternative lengths without spillovers across cycles. Making use of the proposed representations within the classical family of time-varying conditional volatility models, we document the role of time-varying volatility forecasts in generating orthogonal predictive scale-specific cycles in returns. We conclude by providing suggestive evidence that the conditional variances of the predictive return cycles (i) may be priced over short-to-medium horizons and (ii) may offer economically-relevant trading signals over these same horizons.