Time-frequency decomposition and wavelet-based forecasting (bond-retun predictability)

Alexandre Dias de Vasconcelos (Student)

Student thesis: Master's Thesis

Abstract

This thesis investigates whether wavelet-based frequency decomposition can enhance out-of-sample predictability and economic value in forecasting long-term government bond returns. Traditional time-domain models have often struggled to maintain forecasting accuracy when market regimes shift, motivating an exploration of multi-scale methods. Building on studies such as Faria & Verona, 2020, we apply the maximal overlap discrete wavelet transform (MODWT) to decompose various macroeconomic predictors into high-frequency, business-cycle-frequency, and low-frequency components. Out-of-sample forecasts are then generated via an expanding window approach and evaluated against a simple historical-mean benchmark. Our empirical findings reveal that certain predictors, particularly the term spread and book-to-market, exhibit substantially higher out-of-sample 𝑅2 and Certainty Equivalent Return (CER) gains once the most relevant frequency frequencies are isolated. The mean–variance allocation framework demonstrates that wavelet-based forecasts offer notable utility improvements for moderate risk-aversion investors. However, the benefits depend strongly on portfolio weight constraints. Relaxed bounds amplify potential returns (and losses), a purely long-only setting yields modest but stable gains. Overall, these results echo the broader frequency-domain literature (Kim & In, 2005) by underscoring how wavelet-based methods can reveal valuable time-horizon-specific signals for bond-return forecasting, provided that each investor’s risk profile and trading constraints are carefully considered.