Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff

Hong, Seok Young; Linton, Oliver

Abstract

© 2020 Elsevier B.V. This paper studies nonparametric estimation of the infinite order regression E(Ytk|Ft−1), k∈Z with stationary and weakly dependent data. We propose a Nadaraya–Watson type estimator that operates with an infinite number of conditioning variables. We propose a bandwidth sequence that shrinks the effects of long lags, so the influence of all conditioning information is modelled in a natural and flexible way, and the issues of omitted information bias and specification error are effectively handled. We establish the asymptotic properties of the estimator under a wide range of static and dynamic regressions frameworks, thereby allowing various kinds of conditioning variables to be used. We establish pointwise/uniform consistency and CLTs. We show that the convergence rates are at best logarithmic, and depend on the smoothness of the regression, the distribution of the marginal regressors and their dependence structure in a non-trivial way via the Lambert W function. We apply our methodology to examine the intertemporal risk-return relation for the aggregate stock market, and some new empirical evidence is reported. For the S&P 500 daily data from 1950 to 2017 using our estimator we report an overall positive risk-return relation. We also find evidence of strong time variation and counter-cyclical behaviour in risk aversion. These conclusions are possibly attributable to the allowance of further flexibility and the inclusion of otherwise neglected information in our method.

Citation

Hong, S. Y., & Linton, O. (2020). Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff. Journal of Econometrics, 219(2), 389-424. https://doi.org/10.1016/j.jeconom.2020.03.009

• Journal Article Type: Article
• Acceptance Date: Nov 8, 2018
• Online Publication Date: Mar 29, 2020
• Publication Date: 2020-12
• Deposit Date: Nov 13, 2018
• Publicly Available Date: Mar 30, 2022
• Journal: Journal of Econometrics
• Print ISSN: 0304-4076
• Electronic ISSN: 1872-6895
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 219
• Issue: 2
• Pages: 389-424
• DOI: https://doi.org/10.1016/j.jeconom.2020.03.009
• Keywords: Economics and Econometrics; Applied Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/1244704
• Publisher URL: https://www.sciencedirect.com/science/article/abs/pii/S0304407620301044
• Additional Information: This version: 12 June 2018; the Associate Editor and two anonymous referees. We also thank Alexey Rudenko for providing an original Russian photocopy of Sytaya (1974), Hyungjin Lee for translating the paper, and the ERC for providing financial support. 1