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**Measures of conditional linear dependence and feedback between time series.**
*(English)*
Zbl 0553.62083

The author extends the scope of his previous works by introducing measures of linear dependence and feedback for two multiple time series conditional on a third one. Such extension is suitable for various situations in macroeconomics. The measures are non-negative and can be expressed in terms of measures of unconditional feedback between various combinations of the three series.

Moreover, the decomposition of directional conditional linear feedback is suggested. The conditional measures can be estimated by combining the canonical factorization algorithm of Whittle with a parametric bootstrap (point estimates with a first order correction for small sample bias and approximate confidence intervals for these estimates are obtained). The theory is demonstrated by means of an empirical example with real output, money and interest rates.

Moreover, the decomposition of directional conditional linear feedback is suggested. The conditional measures can be estimated by combining the canonical factorization algorithm of Whittle with a parametric bootstrap (point estimates with a first order correction for small sample bias and approximate confidence intervals for these estimates are obtained). The theory is demonstrated by means of an empirical example with real output, money and interest rates.

Reviewer: T.Cipra

### MSC:

62M15 | Inference from stochastic processes and spectral analysis |

91B84 | Economic time series analysis |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62P20 | Applications of statistics to economics |