Conditional Spectral Methods

We model predictive frequency-specific cycles. By employing suitable matrix representations, we express lead values of covariance-stationary multivariate time series in terms of conditionally orthonormal frequency-specific basis. The representations yield conditionally orthogonal decompositions of these lead values. They also provide decompositions of the conditional variances and betas in terms of conditional frequency-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 frequency-specific cycles in returns. We conclude by providing suggestive evidence that the conditional variances of the predictive return cycles may be priced over short-to-medium horizons