Testing diffusion processes for non-stationarity
type: Item
instance of: scholarly article
title: Testing diffusion processes for non-stationarity
zbMATH Open document ID: 1173.91025
author: Jeff Hamrick
author: Murad S. Taqqu
published in: Mathematical Methods of Operations Research
publication date: 2009-07-06T00:00:00Z
full work available at URL: https://repository.usfca.edu/msan_fac/3
review text: Financial data are often assumed to be generated by diffusions. Using recent results of \textit{J. Fan} et al. [J. Am. Stat. Assoc. 102, No. 478, 618--631 (2007; Zbl 1172.62329), J. Financ Econometer, 5, 321--357 (2007)] and a multiple comparisons procedure created by \textit{Y. Benjamini} and \textit{Y. Hochberg} [J. R. Stat. Soc., Ser. B 57, No.1, 289-300 (1995; Zbl 0809.62014)], the authors develop a test for non-stationarity of a one-dimensional diffusion based on the time inhomogeneity of the diffusion function. The procedure uses a single sample path of the diffusion and involves two estimators, one temporal and one spatial. They first apply the test to simulated data generated from a variety of one-dimensional diffusions. They then apply their test to interest rate data and real exchange rate data. The application to real exchange rate data is of particular interest, since a consequence of the law of one price (or the theory of purchasing power parity) is that real exchange rates should be stationary. With the exception of the GBP/USD real exchange rate, they find evidence that interest rates and real exchange rates are generally non-stationary. The software used to implement the estimation and testing procedure is available on demand and its use is described in the paper.
reviewed by: Elisa Alòs
Mathematics Subject Classification ID: 91B70
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 5575942
zbMATH Keywords: nonparametric estimation
zbMATH Keywords: diffusions
zbMATH Keywords: purchasing power parity
zbMATH Keywords: exchange rates
zbMATH Keywords: stationarity
describes a project that uses: TTL
describes a project that uses: RiskMetrics
MaRDI profile type: Publication
OpenAlex ID: W2064125721
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DOI: 10.1007/S00186-008-0250-9
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description: scientific article; zbMATH DE number 5575942