Consistent Local Spectrum Inference for Predictive Return Regressions

Torben G. Andersen*, Rasmus T. Varneskov

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

This paper studies the properties of predictive regressions for asset returns in economic systems governed by persistent vector autoregressive dynamics. In particular, we allow for the state variables to be fractionally integrated, potentially of different orders, and for the returns to have a latent persistent conditional mean, whose memory is difficult to estimate consistently by standard techniques in finite samples. Moreover, the predictors may be endogenous and “imperfect.” In this setting, we develop a consistent local spectrum (LCM) estimation procedure, that delivers asymptotic Gaussian inference. Furthermore, we provide a new LCM-based estimator of the conditional mean persistence, that leverages biased regression slopes as well as new LCM-based tests for significance of (a subset of) the predictors, which are valid even without estimating the return persistence. Simulations illustrate the theoretical arguments. Finally, an empirical application to monthly S&P 500 return predictions provides evidence for a fractionally integrated conditional mean component. Our new LCM procedure and tools indicate significant predictive power for future returns stemming from key state variables such as the default spread and treasury interest rates.
Original languageEnglish
JournalEconometric Theory
Volume38
Issue number6
Pages (from-to)1253-1307
Number of pages55
ISSN0266-4666
DOIs
Publication statusPublished - Dec 2022

Bibliographical note

Published online: 03 August 2022.

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