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Information-theoretic analysis of serial and cointegration. (English) Zbl 1079.62539

Summary: This paper is devoted to presenting wider characterizations of memory and cointegration in time series, in terms of information-theoretic statistics such as the entropy and the mutual information between pairs of variables. We suggest a nonparametric and nonlinear methodology for data analysis and for testing the hypotheses of long memory and the existence of a cointegrating relationship in a nonlinear context. This new framework represents a natural extension of the linear-memory concepts based on correlations. Finally, we show that our testing devices seem promising for exploratory analysis with nonlinearly cointegrated time series.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62B10 Statistical aspects of information-theoretic topics
62P20 Applications of statistics to economics
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