Sequential Change Point Estimation Using Empirical Likelihood for Time Series Data
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Date
2023-09
Authors
Machuka, Carolyne Kemunto
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
Sequential Change point detection has enhanced the reliance on analysis of live data
as it streams into the system to support real-time decision-making processes. This has
played a key role in the advancement of time series modeling and forecasting in financial
time series and risk management. This domain has a growing demand to identify
change points precisely and efficiently for development of automated analytical models.
In this work, sequential change point estimation based on empirical likelihood
test statistic is developed by maximizing the likelihood of the empirical distribution
of the data subject to constraints based on the sample moments. Change point is declared
when the test statistic exceeds a set threshold. The threshold is set such that it
maximises the power of rejecting the null hypothesis. A stop time function is defined
based on the null hypothesis. Consistency of the change point estimator has been verified
through monte carlo simulations based on different sample sizes to demonstrate
the empirical power of the test statistic. As the pre change historical data grew unbounded,
the bias of the Mean Absolute Error (MAE) approaches zero. The estimator
converges closer to the true values. The estimator was fitted on KES/USD exchange
rate data from January 2017 to December 2021.
Description
A Research Project Submitted In Partial Fulfillment of the Requirement for the Award of a Degree of Masters of Science (Statistics) in the School of Pure and Applied Sciences of Kenyatta University, September 2023.
Keywords
Sequential Change Point Estimation, Empirical Likelihood, Time Series Data