Testing diffusion processes for non-stationarity
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.
scientific article; zbMATH DE number 5575942
scientific article