A drunk and her dog: a spurious relation? Cointegration tests as instruments to detect spurious correlations between integrated time series |
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Authors: | Esther Stroe-Kunold Joachim Werner |
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Institution: | 1.Department of Psychology,University of Heidelberg,Heidelberg,Germany |
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Abstract: | A significant correlation between integrated time series does not necessarily imply a meaningful relation. The relation can
also be meaningless, i.e. spurious. Cointegration is sometimes illustrated by the metaphor of ‘a drunk and her dog’. The relation
between integrated processes is meaningful, if they are cointegrated. To prevent spurious correlations, integrated series
are usually transformed. This implies a loss of information. In case of cointegration, these transformations are no longer
necessary. Moreover, it can be shown that cointegration tests are instruments to detect spurious correlations between integrated
time series. This paper compares the Dickey–Fuller and the Johansen cointegration test. By means of Monte Carlo simulations,
we found that these cointegration tests are a much more accurate alternative for the identification of spurious relations
compared to the rather imprecise method of utilizing the R
2-and DW-statistics recommended by some authors. Furthermore, we demonstrate that cointegration techniques are precise methods of
distinguishing between spurious and meaningful relations even if the dependency between the processes is very low. Using these
tests, the researcher is not in danger of either neglecting a small but meaningful relation or regarding a relation as meaningful
which is actually spurious. |
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