Unbalanced Regressions and the Predictive Equation

Daniela Osterrieder, Daniel Ventosa-Santaulària, J. Eduardo Vera-Valdés

Research output: Working paperResearch

Abstract

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.
Original languageEnglish
PublisherAarhus Universitetsforlag
Pages1 - 56
Publication statusPublished - 4 Feb 2015

Fingerprint

Risk process
Risk-return trade-off
Empirical analysis
Data generating process
Statistical inference
Prediction
Predictors
Integrated
Inference
Level shift
Predictive regressions
Instrumental variables
Return predictability

Keywords

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

Cite this

Osterrieder, D., Ventosa-Santaulària, D., & Vera-Valdés, J. E. (2015). Unbalanced Regressions and the Predictive Equation. (pp. 1 - 56). Aarhus Universitetsforlag.
Osterrieder, Daniela ; Ventosa-Santaulària, Daniel ; Vera-Valdés, J. Eduardo. / Unbalanced Regressions and the Predictive Equation. Aarhus Universitetsforlag, 2015. pp. 1 - 56
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Osterrieder, D, Ventosa-Santaulària, D & Vera-Valdés, JE 2015 'Unbalanced Regressions and the Predictive Equation' Aarhus Universitetsforlag, pp. 1 - 56.

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

Aarhus Universitetsforlag, 2015. p. 1 - 56.

Research output: Working paperResearch

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Osterrieder D, Ventosa-Santaulària D, Vera-Valdés JE. Unbalanced Regressions and the Predictive Equation. Aarhus Universitetsforlag. 2015 Feb 4, p. 1 - 56.