### Abstract

Original language | English |
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Publisher | Aarhus Universitetsforlag |

Pages | 1 - 56 |

Publication status | Published - 4 Feb 2015 |

### Fingerprint

### Keywords

- Predictive regression, persistent predictor, fractional integration, regression unbalancedness, IV estimation

### Cite this

*Unbalanced Regressions and the Predictive Equation*. (pp. 1 - 56). Aarhus Universitetsforlag.

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**Unbalanced Regressions and the Predictive Equation.** / Osterrieder, Daniela; Ventosa-Santaulària, Daniel; Vera-Valdés, J. Eduardo.

Research output: Working paper › Research

TY - UNPB

T1 - Unbalanced Regressions and the Predictive Equation

AU - Osterrieder, Daniela

AU - Ventosa-Santaulària, Daniel

AU - Vera-Valdés, J. Eduardo

PY - 2015/2/4

Y1 - 2015/2/4

N2 - Predictive return regressions with persistent regressors are typically plagued by (asymptotically) biased/inconsistent estimates of the slope, non-standard or potentially even spurious statistical inference, and regression unbalancedness. We alleviate the problem of unbalancedness in the theoretical predictive equation by suggesting a data generating process, where returns are generated as linear functions of a lagged latent I(0) risk process. The observed predictor is a function of this latent I(0) process, but it is corrupted by a fractionally integrated noise. Such a process may arise due to aggregation or unexpected level shifts. In this setup, the practitioner estimates a misspecified, unbalanced, and endogenous predictive regression. We show that the OLS estimate of this regression is inconsistent, but standard inference is possible. To obtain a consistent slope estimate, we then suggest an instrumental variable approach and discuss issues of validity and relevance. Applying the procedure to the prediction of daily returns on the S&P 500, our empirical analysis confirms return predictability and a positive risk-return trade-off.

AB - Predictive return regressions with persistent regressors are typically plagued by (asymptotically) biased/inconsistent estimates of the slope, non-standard or potentially even spurious statistical inference, and regression unbalancedness. We alleviate the problem of unbalancedness in the theoretical predictive equation by suggesting a data generating process, where returns are generated as linear functions of a lagged latent I(0) risk process. The observed predictor is a function of this latent I(0) process, but it is corrupted by a fractionally integrated noise. Such a process may arise due to aggregation or unexpected level shifts. In this setup, the practitioner estimates a misspecified, unbalanced, and endogenous predictive regression. We show that the OLS estimate of this regression is inconsistent, but standard inference is possible. To obtain a consistent slope estimate, we then suggest an instrumental variable approach and discuss issues of validity and relevance. Applying the procedure to the prediction of daily returns on the S&P 500, our empirical analysis confirms return predictability and a positive risk-return trade-off.

KW - Predictive regression, persistent predictor, fractional integration, regression unbalancedness, IV estimation

M3 - Working paper

SP - 1

EP - 56

BT - Unbalanced Regressions and the Predictive Equation

PB - Aarhus Universitetsforlag

ER -