statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

and

econometrics Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics", '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...

, asymmetric cointegration describes a long-term relationship between variables where positive and negative shocks to the equilibrium have different impacts. This builds upon the concept of

cointegration In econometrics, cointegration is a statistical property describing a long-term, stable relationship between two or more time series variables, even if those variables themselves are individually non-stationary (i.e., they have trends). This means ...

, which refers to a long-term, stable relationship between two or more variables, even if those variables individually fluctuate over time. For example, consider the price of a

commodity In economics, a commodity is an economic goods, good, usually a resource, that specifically has full or substantial fungibility: that is, the Market (economics), market treats instances of the good as equivalent or nearly so with no regard to w ...

and the price of a related

derivative In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is t ...

. While both prices might fluctuate daily, they are expected to maintain a long-term equilibrium relationship. However, a sudden increase in the commodity price might lead to a faster adjustment in the derivative price than a sudden decrease. This difference in adjustment speeds would be an example of asymmetric cointegration. Because standard cointegration tests assume symmetric adjustment, they may fail to detect asymmetric cointegration. Therefore, specialized tests, such as threshold autoregressive and momentum-threshold cointegration tests, are employed to investigate for this asymmetry. These tests help determine if the adjustment process back to equilibrium differs depending on the direction of the deviation.

References

{{reflist Statistical hypothesis testing Time series Econometrics