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

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.