Johansenmetoden

Johansenmetoden, also known as the Johansen test, is a statistical procedure used in econometrics to determine the number of cointegrating relationships among a set of time series variables. Cointegration describes a situation where two or more non-stationary time series have a long-run equilibrium relationship. If series are cointegrated, they will tend to move together over time, and any deviation from this long-run relationship is temporary.

The Johansen test is particularly useful because it can identify multiple cointegrating relationships, unlike simpler tests that only consider pairs of variables. The test is based on a vector error correction model (VECM). It involves estimating the rank of a specific matrix, which corresponds to the number of cointegrating vectors. The procedure provides two main statistics: the trace statistic and the maximum eigenvalue statistic. Both statistics are used to test hypotheses about the number of cointegrating relationships, ranging from zero up to the number of variables minus one.

When applying the Johansen test, selecting the appropriate lag length for the VECM is crucial, as it can influence the test results. Furthermore, the test assumes that the time series are integrated of order one, meaning they are non-stationary but become stationary after differencing once. The Johansen test is widely used in empirical finance and macroeconomics to study relationships between variables such as interest rates, inflation, and exchange rates.