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**Understanding spurious regressions in econometrics.**
*(English)*
Zbl 0602.62098

Regression equations which relate two or more time series represented by integrated random processes of the ARIMA type, frequently have \(R^ 2\) yet display highly autocorrelated residuals indicated by very low Durban- Watson statistics. In such situations the usual signficance tests on the regression coefficients are very misleading.

The present paper develops an asymptotic theory for such regressions, which explains as a special case the spurious regressions where the usual t-ratio significance test is shown to diverge as the sample size gets infinitely large. This asymptotic theory is also extended to multiple regressions where the variables are generated by a general vector integrated process.

The present paper develops an asymptotic theory for such regressions, which explains as a special case the spurious regressions where the usual t-ratio significance test is shown to diverge as the sample size gets infinitely large. This asymptotic theory is also extended to multiple regressions where the variables are generated by a general vector integrated process.

Reviewer: J.K.Sengupta

### MSC:

62P20 | Applications of statistics to economics |

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

91B84 | Economic time series analysis |

### Keywords:

cointegrating regressions; F-ratio test; coefficient of determination; Box-Pierce statistic; regression diagnostics; integrated random processes; ARIMA; autocorrelated residuals; asymptotic theory; spurious regressions; t-ratio significance test; multiple regressions; vector integrated process### References:

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