Consistent Inference for Predictive Regressions in Persistent Economic Systems

91 Pages Posted: 2 Apr 2019 Last revised: 15 Nov 2019

See all articles by Torben G. Andersen

Torben G. Andersen

Northwestern University - Kellogg School of Management; National Bureau of Economic Research (NBER); Aarhus University - CREATES

Rasmus Tangsgaard Varneskov

Copenhagen Business School - Department of Finance; Nordea Bank AB - Nordea Asset Management

Date Written: November 14, 2019

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 $\chi^2$-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.

Keywords: Endogeneity Bias, Fractional Integration, Frequency Domain Inference, Hypothesis Testing, Spurious Inference, Stochastic Volatility, VAR Models

JEL Classification: C13, C14, C32, C52, C53, G12

Suggested Citation

Andersen, Torben G. and Varneskov, Rasmus Tangsgaard, Consistent Inference for Predictive Regressions in Persistent Economic Systems (November 14, 2019). Available at SSRN: https://ssrn.com/abstract=3359946 or http://dx.doi.org/10.2139/ssrn.3359946