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초록
영어
This paper provides estimators of the realized third and fourth order (joint) cumulants, which are standardized (co)moments, for arithmetic returns with one assumption under which each price is a martingale. The estimators that are developed based on Aggregation Property of Neuberger (2012) help to access the ex-post moments of returns for a specific period and do not require data for a long period. Moreover, we show that neither realized fourth moments nor third comoments of log returns exist under the similar condition. In addition, we conduct an empirical study based on the realized higher order cumulants and the results are consistent with the literature.
목차
Abstract
I. Introduction
II. The Aggregation Property Given Comoment Processes
III. Practical issues on the estimation
IV. Empirical study
IV.1. Cumulants of the S&P 500 returns
IV.2. (Joint) cumulants of returns and subsequent returns
V. Concluding Remark
Appendix A: Proofs of Proposition 1 and 2.
Appendix B: Proofs of Proposition 3 and 5 and Corollary 4.
References
I. Introduction
II. The Aggregation Property Given Comoment Processes
III. Practical issues on the estimation
IV. Empirical study
IV.1. Cumulants of the S&P 500 returns
IV.2. (Joint) cumulants of returns and subsequent returns
V. Concluding Remark
Appendix A: Proofs of Proposition 1 and 2.
Appendix B: Proofs of Proposition 3 and 5 and Corollary 4.
References
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자료제공 : 네이버학술정보