VAR Models, Cointegration and Mixed-Frequency Data

Sammanfattning: This thesis consists of five papers that study two aspects of vector autoregressive (VAR) modeling: cointegration and mixed-frequency data.Paper I develops a method for estimating a cointegrated VAR model under restrictions implied by the economy under study being a small open economy. Small open economies have no influence on surrounding large economies. The method suggested by Paper I provides a way to enforce the implied restrictions in the model. The method is illustrated in two applications using Swedish data, and we find that differences in impulse responses resulting from failure to impose the restrictions can be considerable.Paper II considers a Bayesian VAR model that is specified using a prior distribution on the unconditional means of the variables in the model. We extend the model to allow for the possibility of mixed-frequency data with variables observed either monthly or quarterly. Using real-time data for the US, we find that the accuracy of the forecasts is generally improved by leveraging mixed-frequency data, steady-state information, and a more flexible volatility specification.The mixed-frequency VAR in Paper II is estimated using a state-space formulation of the model. Paper III studies this step of the estimation algorithm in more detail as the state-space step becomes prohibitive for larger models when the model is employed in real-time situations. We therefore propose an improvement of the existing sampling algorithm. Our suggested algorithm is adaptive and provides considerable improvements when the size of the model is large. The described approach makes the use of large mixed-frequency VARs more feasible for nowcasting.Paper IV studies the estimation of large mixed-frequency VARs with stochastic volatility. We employ a factor stochastic volatility model for the error term and demonstrate that this allows us to improve upon the algorithm for the state-space step further. In addition, regression parameters can be sampled independently in parallel. We draw from the literature on large VARs estimated on single-frequency data and estimate mixed-frequency models with 20, 34 and 119 variables.Paper V provides an R package for estimating mixed-frequency VARs. The package includes the models discussed in Paper II and IV as well as additional alternatives. The package has been designed with the intent to make the process of specification, estimation and processing simple and easy to use. The key functions of the package are implemented in C++ and are available for other packages to use and build their own mixed-frequency VARs.