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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.
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
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