A nonparametric predictive regression model using partitioning estimators based on Taylor expansions
A nonparametric predictive regression model using partitioning estimators based on Taylor expansions
This article proposes a nonparametric predictive regression model. The unknown function modeling the predictive relationship is approximated using polynomial Taylor expansions applied over disjoint intervals covering the support of the predictor variable. The model is estimated using the theory on partitioning estimators that is extended to a stationary time series setting. We show pointwise and uniform convergence of the proposed estimator and derive its asymptotic normality. These asymptotic results are applied to test for the presence of predictive ability. We develop an asymptotic pointwise test of predictive ability using the critical values of a Normal distribution, and a uniform test with asymptotic distribution that is approximated using a p-value transformation and Wild bootstrap methods. These theoretical insights are illustrated in an extensive simulation exercise and also in an empirical application to forecasting high-frequency based realized volatility measures. Our results provide empirical support to the presence of nonlinear autoregressive predictability of these measures for the constituents of the Dow Jones index.
Series estimators, Taylor expansions, asymptotic theory, realized volatility, time series predictability
Olmo, Jose
706f68c8-f991-4959-8245-6657a591056e
17 October 2022
Olmo, Jose
706f68c8-f991-4959-8245-6657a591056e
Olmo, Jose
(2022)
A nonparametric predictive regression model using partitioning estimators based on Taylor expansions.
Journal of Time Series Analysis.
(doi:10.1111/jtsa.12668).
Abstract
This article proposes a nonparametric predictive regression model. The unknown function modeling the predictive relationship is approximated using polynomial Taylor expansions applied over disjoint intervals covering the support of the predictor variable. The model is estimated using the theory on partitioning estimators that is extended to a stationary time series setting. We show pointwise and uniform convergence of the proposed estimator and derive its asymptotic normality. These asymptotic results are applied to test for the presence of predictive ability. We develop an asymptotic pointwise test of predictive ability using the critical values of a Normal distribution, and a uniform test with asymptotic distribution that is approximated using a p-value transformation and Wild bootstrap methods. These theoretical insights are illustrated in an extensive simulation exercise and also in an empirical application to forecasting high-frequency based realized volatility measures. Our results provide empirical support to the presence of nonlinear autoregressive predictability of these measures for the constituents of the Dow Jones index.
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Accepted/In Press date: 10 October 2022
e-pub ahead of print date: 17 October 2022
Published date: 17 October 2022
Additional Information:
Funding Information:
Jose Olmo acknowledges financial support from project PID2019‐104326GB‐I00 from Ministerio de Ciencia e Innovación and from Fundación Agencia Aragonesa para la Investigación y el Desarrollo (ARAID).
Publisher Copyright:
© 2022 John Wiley & Sons Ltd.
Keywords:
Series estimators, Taylor expansions, asymptotic theory, realized volatility, time series predictability
Identifiers
Local EPrints ID: 470919
URI: http://eprints.soton.ac.uk/id/eprint/470919
ISSN: 0143-9782
PURE UUID: e82110dc-80c2-491b-99cf-6244291f62fb
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Date deposited: 21 Oct 2022 16:30
Last modified: 17 Mar 2024 07:34
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