Consistent inference for predictive regressions in persistent economic systems

TY - JOUR

T1 - Consistent inference for predictive regressions in persistent economic systems

AU - Andersen, Torben G.

AU - Varneskov, Rasmus T.

N1 - Funding Information: We wish to thank the managing editor Serena Ng, an anonymous referee, Anna Cieslak, Ian Dew-Becker, Christian Konrad, Daniela Osterrieder, Peter C.B. Phillips, Pavol Povala, Eric Renault, Barbara Rossi, Ivan Shaliastovich, Katsumi Shimotsu, Jim Stock, George Tauchen, Allan Timmermann, Fabio Trojani along with participants at various seminars and conferences for helpful comments and suggestions. Note that some of this material in this manuscript supersede a former manuscript entitled “Inference in Intertemporal Asset Pricing Models with Stochastic Volatility and the Variance Risk Premium”. Financial support from CREATES , Center for Research in Econometric Analysis of Time Series ( DNRF78 ), funded by the Danish National Research Foundation , is gratefully acknowledged. Publisher Copyright: © 2020 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2021/9

Y1 - 2021/9

N2 - 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.

AB - 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.

KW - Endogeneity bias

KW - Fractional integration

KW - Frequency domain inference

KW - Hypothesis testing

KW - Spurious inference

KW - Stochastic volatility

KW - VAR models

UR - http://www.scopus.com/inward/record.url?scp=85096094265&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2020.04.051

DO - 10.1016/j.jeconom.2020.04.051

M3 - Journal article

AN - SCOPUS:85096094265

SN - 0304-4076

VL - 224

SP - 215

EP - 244

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 1

ER -