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Testing diffusion processes for non-stationarity

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  • Jeff Hamrick
  • Murad Taqqu

Abstract

Financial data are often assumed to be generated by diffusions. Using recent results of Fan et al. (J Am Stat Assoc, 102:618–631, 2007; J Financ Econometer, 5:321–357, 2007) and a multiple comparisons procedure created by Benjamini and Hochberg (J R Stat Soc Ser B, 59:289–300, 1995), we 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. We first apply the test to simulated data generated from a variety of one-dimensional diffusions. We then apply our 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, we 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 we describe its use in the paper. Copyright Springer-Verlag 2009

Suggested Citation

  • Jeff Hamrick & Murad Taqqu, 2009. "Testing diffusion processes for non-stationarity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 509-551, July.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:3:p:509-551
    DOI: 10.1007/s00186-008-0250-9
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    References listed on IDEAS

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    1. Johan Walden, 2017. "Recovery with Unbounded Diffusion Processes," Review of Finance, European Finance Association, vol. 21(4), pages 1403-1444.

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