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Nonlinear autocorrelograms: an application to inter-trade durations. (English) Zbl 1062.62177

This paper introduces some approaches to study serial correlation problems encountered in empirical analysis. The authors examine effects of predetermined nonlinear parametric transformations on autocorrelation values and the persistence range of transformed series. The considered methods emphasize the consequences of transformations applied to long memory processes, like series of squared returns and inter-trade durations. In particular, an invariance property for the order of fractional integration with respect to transformations is introduced which can be used for hypothesis testing. Within the given class of parametric transformations the authors identify parameter values maximizing serial correlation of transformed processes and describe their asymptotic properties.
Another problem concerns transformations that belong to the same class and differ in terms of parameter values which can be selected so as to maximize cross-correlation of transformed series at various lags. The authors search for nonlinear transformations, called canonical transformations, which maximize serial correlation of the transformed series.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics
91B99 Mathematical economics

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