### Abstract

conclusions may be premature. In fact, if anything, our results suggest the reverse causality, i.e., rising volatility predates adverse innovations to key macroeconomic variables. Simulations are employed to illustrate the relevance of the theoretical arguments for finite-sample inference.

Original language | English |
---|---|

Place of Publication | Aarhus |

Publisher | Aarhus Universitet |

Number of pages | 62 |

Publication status | Published - 2018 |

Series | Creates Research Paper |
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Number | 2018-9 |

### Keywords

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

### Cite this

*Consistent Inference for Predictive Regressions in Persistent VAR Economies*. Aarhus: Aarhus Universitet. Creates Research Paper, No. 2018-9

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**Consistent Inference for Predictive Regressions in Persistent VAR Economies.** / Andersen, Torben G. ; Varneskov, Rasmus T.

Research output: Working paper › Research

TY - UNPB

T1 - Consistent Inference for Predictive Regressions in Persistent VAR Economies

AU - Andersen, Torben G.

AU - Varneskov, Rasmus T.

PY - 2018

Y1 - 2018

N2 - This paper studies the properties of standard predictive regressions in model economies, characterized through persistent vector autoregressive dynamics for the state variables and the associated series of interest. In particular, we consider a setting where all, or a subset, of the variables may be fractionally integrated, and note that this induces a spurious regression problem. We then propose a new inference and testing procedure – the local spectrum (LCM) approach – for the joint significance of the regressors, which is robust against the variables having different integration orders. The LCM procedure is based on (semi-)parametric fractional-filtering and band spectrum regression using a suitably selected set of frequency ordinates. We establish the asymptotic properties and explain how they differ from and extend existing procedures. Using these new inference and testing techniques, we explore the implications of assuming VAR dynamics in predictive regressions for the realized return variation. Standard least squares predictive regressions indicate that popular financial and macroeconomic variables carry valuable information about return volatility. In contrast, we find no significant evidence using our robust LCM procedure, indicating that priorconclusions may be premature. In fact, if anything, our results suggest the reverse causality, i.e., rising volatility predates 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 the properties of standard predictive regressions in model economies, characterized through persistent vector autoregressive dynamics for the state variables and the associated series of interest. In particular, we consider a setting where all, or a subset, of the variables may be fractionally integrated, and note that this induces a spurious regression problem. We then propose a new inference and testing procedure – the local spectrum (LCM) approach – for the joint significance of the regressors, which is robust against the variables having different integration orders. The LCM procedure is based on (semi-)parametric fractional-filtering and band spectrum regression using a suitably selected set of frequency ordinates. We establish the asymptotic properties and explain how they differ from and extend existing procedures. Using these new inference and testing techniques, we explore the implications of assuming VAR dynamics in predictive regressions for the realized return variation. Standard least squares predictive regressions indicate that popular financial and macroeconomic variables carry valuable information about return volatility. In contrast, we find no significant evidence using our robust LCM procedure, indicating that priorconclusions may be premature. In fact, if anything, our results suggest the reverse causality, i.e., rising volatility predates 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

KW - Endogeneity bias

KW - Fractional integration

KW - Frequency domain inference

KW - Hypothesis testing

KW - Spurious inference

KW - VAR models

M3 - Working paper

BT - Consistent Inference for Predictive Regressions in Persistent VAR Economies

PB - Aarhus Universitet

CY - Aarhus

ER -