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 processReferences:
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