Realized Multi-Power Variation Process for Jump Detection in the Nigerian All Share Index

Article Sidebar

PDF
Published: Aug 1, 2021
DOI: https://doi.org/10.5556/j.tkjm.52.2021.3497
Keywords:
Bipower variation; Continuous Semi-martingale; Integrated variance; Jumps; Convergence.

Main Article Content

Mabel Adeosun
OSUN STATE COLLEGE OF TECHNOLOGY, ESA-OKE. OSUN-OSUN
Olabisi Ugbebor
Mathematics Department, University of Ibadan, Ibadan. Nigeria.
https://orcid.org/0000-0002-7099-953X

Abstract

In this paper, we studied the particular cases of higher-order realized multipower variation process, their asymptotic properties comprising the probability limits and limit distributions were highlighted. The respective asymptotic variances of the limit distributions were obtained and jump detection models were developed from the asymptotic results. The models were obtained from the particular cases of the higher-order of the realized multipower variation process, in a class of continuous stochastic volatility semimartingale process. These are extensions of the method of jump detection by Barndorff-Nielsen and Shephard (2006), for large discrete data. An Empirical Application of the models to the Nigerian All Share Index (NASI) data shows that the models are robust to jumps and suggest that stochastic models with added jump components will give a better representation of the NASI price process.

Article Details

How to Cite
Adeosun, M., & Ugbebor, O. (2021). Realized Multi-Power Variation Process for Jump Detection in the Nigerian All Share Index. Tamkang Journal of Mathematics, 52(3), 397–412. https://doi.org/10.5556/j.tkjm.52.2021.3497
Issue
Vol. 52 No. 3 (2021)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Author Biography

Olabisi Ugbebor, Mathematics Department, University of Ibadan, Ibadan. Nigeria.

Professor of Mathematics, Mathematics Departmet, Faculty of Science University of Ibadan, Ibadan, Nigeria.

References

A. A. Salisu. Comparative Performance of volatility models for the Nigeria stock market.The Empirical Economics Letter, 11(2):121–130, 2012.

O. S. Yaya. Nigeria Stock Index: A search for Optimal GARCH model using High FrequencyData. Journal of Applied Statistics, 4(2):69–85, 2013.

N. V. Atoi. Testing Volatility in Nigeria Stock Market using GARCH models. Applied Statistics, 5(2):65–85, 2014.

O. S. Yaya and L. A. Gil-Alana. The persistence asymmetric Volatility in the Nigeria Stocks Bull and Bear Markets. Economic Modelling, 38:463–469, 2014.

M. E. Adeosun, S. O. Edeki and O. O. Ugbebor. Stochastic analysis of stock market price models: A case study of Nigeria Stock Exchange. WSEAS Transactions on Mathematics, 14:353–363, 2015.

O. S. Yaya, A. S. Bada and N. V. Atoi. Volatility in the Nigeria stock market: EmpiricalApplication of Beta-t-GARCH. CBN Journal of Applied Statistics, 7(2):27–48, 2016.

A. A. Salisu. Modelling oil prices volatility with the beta-skew-t-e garch framework. Economics Bulletin, 36(3):1315–1324, 2016.

O. E. Barndorff-Nielsen and N. Shephard. Realized Power variation and Stochastic Volatility Models. Bernoulli, 8(2):243–265, 2003.

J. Jacod and A. N. Shiryaev. Limit Theorems for Stochastic Processes. Springer-Verlag, Second Edition, vol. 288, 2003.

J. Yan, J. He and S. Wang. Semimartingale Theory and Stochastic Calculus. Science Press, CRC Press Inc., 1992.

O. E. Barndorff-Nielsen, S. E. Graversen, J. Jacod and N. Shephard. Limit theorems for bipower variation in Financial Econometrics. Econometrics Theory, 22:677–719, 2006.

J. Jacod. Asymptotic properties of realized power variations and related functionals of Semimartingales. Stochastic Processes and their Applications, 118:517–559, 2008.

Y. A¨ıt-Sahalia and J. Jacod. Testing for jumps in a discretely observed process. The Annals of Statistics, 37(1):184–222, 2009.

O. E. Barndorff-Nielsen, S.E. Graversen, J. Jacod, M. Podolskij and N. Shephard. From Stochastic Calculus to Mathematical Finance, chapter A central limit theorem for realized power and bipower variations of continuous semimartingales, pages 33–68. The Shiryaev Festschrift, Springer-Verlag, Berlin, 2006.

S. Kinnebrock and M. Podolskij. A note on the central limit theorem for bipower variation of general functions. Stochastic Processes and their Applications, 118:1056–1070, 2008.

O. E. Barndorff-Nielsen and N. Shephard. Power and Bipower variation with Stochastic Volatility and Jumps. Journal of Financial Econometrics, 2:1–48, 2004.

O. E. Barndorff-Nielsen and N. Shephard. Econometrics of Testing for Jumps in Financial Economics using Bipower Variation. Journal of Financial Econometrics, 4(1):1–30, 2006.

O. E. Barndorff-Nielsen, N. Shephard and M. Winkel. Limit theorems for multipowervariation in the presence of jumps. Stochastic processes and Applications, 116:796–806,2006.

O. E. Barndorff-Nielsen, S. E. Graversen, J. Jacod, M. Podolskij and N. Shephard. A central limit theorem for realised power and bipower variations of continuous semimartingales. In From stochastic calculus to mathematical finance, pages 33–68. Springer, 2006.

C. Ysusi. Detecting jumps in high-frequency financial series using multipower variation. Banco de Mexico, pages 2006–10, 2006.

D. Lamberton and B. Lapeyre. Introduction to Stochastic Calculus Applied to Finance.Chapman and Hall/CRC Financial Mathematics Series, 2nd edition, 2007.

X. Weijun, L. Guifang and L. Hongyi. A novel jump diffusion model based on ”SGT” distribution and its applications. Economic Modelling, 59:74–92, 2016.

T.G. Andersen, T. Bollerslev and F.X. Diebold. Some like it smooth and some like it rough. Technical report, Northern University, 2010.

X. Haung and G. Tauchen. The Relative Contribution of Jumps to total Price variance. Journal of Financial Econometrics, 4:456–499, 2006.

O. E. Barndorff-Nielsen and N. Shephard. Realized power variation and stochastic volatility. Bernoulli, Vol, 9:243–265, 2003.