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Inference for a change‐point problem under an OU setting with unequal and unknown volatilities
Author(s) -
Chen Fuqi,
Mamon Rogemar,
Nkurunziza Sévérien
Publication year - 2020
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11522
Subject(s) - estimator , consistency (knowledge bases) , econometrics , inference , series (stratigraphy) , point process , point (geometry) , flexibility (engineering) , computer science , estimation , mathematics , statistics , algorithm , economics , artificial intelligence , paleontology , geometry , management , biology
An Ornstein–Uhlenbeck (OU) process is employed as a versatile model to capture the mean‐reverting and stochastic evolution of many variables in various fields of applications including finance and economics. Within the OU setting, we develop a new estimation method to determine the unknown change‐point location under the assumption that the volatilities before and after the change point in a time series are unequal. Our method hinges on the concept of a weighted least sum of squared errors approach and enhanced by a fusion of an iterative algorithm. The consistency of the change‐point estimator is established. This article highlights a numerical implementation on simulated and observed financial market data demonstrating the significant flexibility and accuracy of our proposed modelling and estimation method. The Canadian Journal of Statistics 48: 62–78; 2020 © 2019 Statistical Society of Canada