A Vector Error Correction Model (VECM) is a statistical model used for analyzing non-stationary time series data that are cointegrated. Cointegration refers to the situation where a set of non-stationary series move together over time, suggesting a long-term equilibrium relationship despite short-term fluctuations. The VECM helps to capture both the short-term dynamics and the long-term relationships between these series, allowing for better forecasting and understanding of their interactions.
In practical terms, VECM operates by incorporating both the levels of the non-stationary variables and their differences to account for short-term changes. For example, consider two economic time series, such as GDP and unemployment rates. While both may exhibit trends over time, there may be an underlying relationship that keeps them in equilibrium. VECM can capture this relationship by modeling how deviations from the long-term equilibrium eventually adjust back to it. This model outputs coefficients that reflect not only the impact of changes in one variable on the others but also how quickly the system returns to equilibrium after a shock.
To use a VECM, developers typically start by testing for cointegration among the series, often using techniques such as the Johansen test. Once cointegration is established, the VECM can be estimated, enabling users to analyze how variables interact over the short term while considering their long-term equilibrium. This model is especially useful in fields like economics and finance, where understanding relationships between multiple time series can inform decision-making, policy formulation, and risk management.