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Mixing Integration Orders in Time Series Doesn't Increase Error Risk, New Study Shows
Insights from the Field
Error Correction Model (ECM)
ARDL
Orders Integration
Time Series Analysis
Methodology
PSR&M
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Dataverse
Detecting True Relationships in Time Series Data With Different Orders of Integration was authored by Peter K. Enns, Christopher Wlezien and Carolina Moehlecke. It was published by Cambridge in PSR&M in 2022.

New research clarifies a persistent confusion about mixing integration orders in time series analysis. Contrary to common belief that combining different integration orders leads to inflated type I errors when using General Error Correction/ARDL models, the paper demonstrates these mixed orders don't inherently increase error risks if equations remain balanced.

### Previous Confusion

* Researchers often conflate equation balance requirements with restrictions on mixing variable integration levels.

* This misunderstanding has limited confidence in applying flexible time series modeling techniques.

Our contribution addresses this gap by showing that properly balanced GECM/ADL models can still identify true relationships across variables of differing integration orders. Using both asymptotic analysis and computer simulations, we reveal that while estimation challenges exist due to finite sample issues, researchers typically reach correct inferences when following best practices—model selection based on data characteristics plus rigorous assumption testing.

This finding has significant implications for political science research relying on time series methods. It suggests scholars can confidently use these models without fear of increased error rates from mixed integration orders, provided they maintain proper equation balance and adhere to standard estimation protocols.

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Political Science Research & Methods
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