a. Orthogonalized impulse response functions: Orthogonalized impulse response functions are a statistical tool used to analyze the response of a variable to a shock in a vector autoregressive (VAR) model. The impulse response function shows how the variable responds to a one-time shock to another variable in the system. Orthogonalized impulse response functions are used to eliminate the contemporaneous correlation between the variables in the VAR model, which can make it difficult to interpret the results.
b. Forecast error variance decomposition: Forecast error variance decomposition is a statistical tool used to analyze the contribution of each variable in a VAR model to the forecast error variance of all the variables in the system. It shows how much of the forecast error variance of each variable is due to its own shocks and how much is due to the shocks of the other variables in the system. Forecast error variance decomposition is useful for understanding the relative importance of each variable in the VAR model and for identifying the variables that are driving the forecast error variance.
c. Cointegration: Cointegration is a statistical property of time series data that indicates a long-term relationship between two or more non-stationary variables. Cointegration is important because it allows us to model the long-term relationship between variables even if they are individually non-stationary. Cointegration is often used in econometrics to model the relationship between economic variables that are not stationary, such as GDP and inflation.
d. Speed of adjustment: Speed of adjustment is a measure of how quickly a variable returns to its long-run equilibrium after a shock. In econometrics, speed of adjustment is often used to model the adjustment process of a variable to changes in another variable in a VAR model. Speed of adjustment is important because it allows us to understand how quickly the system returns to equilibrium after a shock and how long it takes for the effects of the shock to dissipate.