Consistent Inference for Predictive Regressions in Persistent Economic Systems

Torben G. Andersen, Rasmus T. Varneskov*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

This paper studies standard predictive regressions in economic systems governed by persistent vector autoregressive dynamics for the state variables. In particular, all – or a subset – of the variables may be fractionally integrated, which induces a spurious regression problem. We propose a new inference and testing procedure – the Local speCtruM (LCM) approach – for joint significance of the regressors, that is robust against the variables having different integration orders and remains valid regardless of whether predictors are significant and, if they are, whether they induce cointegration. Specifically, the LCM procedure is based on fractional filtering and band spectrum regression using a suitably selected set of frequency ordinates. Contrary to existing procedures, we establish a uniform Gaussian limit theory and a standard χ2-distributed test statistic. Using the LCM inference and testing techniques, we explore predictive regressions for the realized return variation. Standard least squares inference indicates that popular financial and macroeconomic variables convey valuable information about future return volatility. In contrast, we find no significant evidence using our robust LCM procedure. If anything, our tests support a reverse chain of causality, with rising financial volatility predating adverse innovations to key macroeconomic variables. Simulations are employed to illustrate the relevance of the theoretical arguments for finite-sample inference.
Original languageEnglish
JournalJournal of Econometrics
Number of pages30
ISSN0304-4076
DOIs
Publication statusPublished - 13 Nov 2020

Bibliographical note

Epub ahead of print. Published online: 13 November 2020.

Keywords

  • Endogeneity bias
  • Fractional integration
  • Frequency domain inference
  • Hypothesis testing
  • Spurious inference
  • Stochastic volatility
  • VAR models

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