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Convergence of a Randomised Change Point Estimator in GARCH Models
Department of Mathematics and Statistics, Pan African University, Nairobi, Kenya
Department of Statistics and Actuarial Science, JKUAT, Nairobi, Kenya
School of Mathematics, University of Nairobi, Nairobi, Kenya
- 1 Department of Mathematics and Statistics, Pan African University, Nairobi, Kenya
- 2 Department of Statistics and Actuarial Science, JKUAT, Nairobi, Kenya
- 3 School of Mathematics, University of Nairobi, Nairobi, Kenya
Journal of Mathematical Finance·Volume 11 (2021)·Pages 234–245·Published 1 March 2021·DOI10.4236/jmf.2021.112013
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Abstract
In this paper, the randomised pseudolikelihood ratio change point estimator for GARCH models in [1] is employed and its limiting distribution is derived as the supremum of a standard Brownian bridge. Data analysis to validate the estimator is carried out using the United states dollar (USD)-Ghana cedi (GHS) daily exchange rate data. The randomised estimator is able to detect and estimate a single change in the variance structure of the data and provides a reference point for historic data analysis.
KeywordsGARCHRandomisedLimiting DistributionBrownian BridgeVolatilityCUSUMIGARCHSupremum
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