An application on Lasso VAR and VARX models

It is known that vector autoregression (VAR) is an effective method for modeling and estimating the common dynamics of macroeconomic time series. The main problem that prevents the applicability of VAR is that it has heavy parameters. That is, the parameter field grows from the second order with the number of series included in the series by rapidly consuming the current series. Furthermore, the estimation of high-dimensional macroeconomic parameters by VAR is a challenging process. Traditional methods that allow the estimation of large VARs either tend to require specific subjective specifications or are not feasible for calculation. At the same time, global economies are becoming increasingly complex. It is of great importance to take into account the stochastic, unmodified external variables in such a complex process. These external variables are included in the models by VARX method. VARX estimates the VAR by including the unmodified external variables in the model. VARX-L, a structured family of the VARX model, enables us to achieve more efficient and healthy results in higher dimensional estimates. The VARX-L adapts several important scalar regression techniques to a vector time series context to greatly reduce the parameter field of the VAR and VARX models. VARX-L demonstrates its effectiveness in both low and high dimensional macroeconomic estimation applications and simulated data samples. In this thesis, one of the punished estimators of VARX-L, "Basic Lasso L, is used to estimate the high-dimensional models using the BigVAR package in the R program. Estimation results are compared using the same data for VAR and VARX models. Keywords: VAR, VARX, VARX-L, BigVAR