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Nuisance parameter free properties of correlation integral based statistics. (English) Zbl 0905.62118
This paper studies conditions under which statistics based on the correlation integral are invariant to the use of estimated residuals from dynamic models. By extending results of B. V. Sukhatme [Ann. Math. Statistics 29, 60-78 (1958; Zbl 0085.35405)] and R. H. Randles [Ann. Stat. 10, 462-474 (1982; Zbl 0493.62022)], we deal directly with the non-smooth indicator kernel. The methods are applied to a popular test of nonlinearity, the so-called BDS test [see W. A. Brock et al., Econ. Rev. 15, No. 3, 197-235 (1996; Zbl 0893.62034)] under a variety of data-generating processes. Furthermore, the extension to other correlation integral-based statistics seems quite straightforward.

MSC:
62P20 Applications of statistics to economics
91B84 Economic time series analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
Software:
KernSmooth
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