Multivariate, penalized models

Vector Error Correction Models are useful for data sets with long-run relationships (also called cointegration). VECMs are useful for estimating both short-term and long-term effects of one-time series on another. The term error-correction relates to the fact that last period’s deviation from a long-run equilibrium, the error, influences its short-run dynamics. These models estimate, besides the long-run relationships between variables, also directly the speed at which a dependent variable returns to equilibrium after a change in other variables. This version is combined with Lasso, Least Absolute Shrinkage, and Selection Operator which forces certain coefficients to be set to zero, effectively choosing a simpler model that does not include those coefficients.

The elastic net is a regression method that linearly combines the lasso and ridge (see below) methods. Basically, the elastic net method finds the ridge regression coefficients, and then does a lasso type shrinkage of the coefficients.

Lasso, Least Absolute Shrinkage and Selection Operator is the most successful application of AI within econometrics. Lasso was introduced in order to improve the prediction accuracy and interpretability of regression models by altering the model fitting process to select only a subset of the provided independent variables for use in the final model rather than using all of them. Lasso forces certain coefficients to be set to zero, effectively choosing a simpler model that does not include those coefficients.

This is a way of using Bayesian models in a VAR framework. Prior to Lasso, the most widely used method for choosing which variables to include was stepwise selection. At that time, ridge regression was the most popular alternative technique used for improving prediction accuracy. Ridge regression improves prediction error by shrinking large regression coefficients in order to reduce overfitting, but it does not perform variable selection and therefore does not help to make the model more interpretable.