19 April 2019
19 April 2019
18 April 2019
This paper reviews estimation and forecasting with Bayesian vector autoregressions (BVARs). In the first part of the paper, we propose a clear classification of the most frequently used prior distributions and we show how the parameters of posterior distributions can be computed for the priors we consider in the paper. A separate section describes the endogenous choice of prior hyperparameters that is currently a key step to estimate a BVAR in a data-rich environment.
The second part of this paper is devoted to forecasting with BVARs. We review both point and density forecasting.
We also developed a package bvarr for statistical environment R with the same notations as in this review. The bvarr package can be freely used for research and educational purposes.
This paper compares the forecasting performance of random walk, frequentist vector autoregression (VAR), and Bayesian vector autoregression with Minnesota prior (BVAR) models on quarterly Russian data sample running from 1995 to 2014. Maximal number of variables included in the model is equal to 14 that requires an endogenous search of optimal shrinkage hyperparameter. The search procedure follows [Bańbura et al., 2010] and [Bloor and Matheson, 2011]. According to the selection method the shrinkage hyperparameter equates the forecasting quality of the frequentist VAR and BVAR for the minimal considered dimension of the model (three variables). For any dimension of the BVAR model the optimal shrinkage hyperparameter is robust to considered functions of relative forecasting accuracy.
We show that the BVAR provides a more accurate forecast than the frequentist VAR on the studied sample. For key macro indicators (the industrial production index, consumer price index and the interbank interest rate), forecasting horizons, and all model sizes, the mean squared error of the BVAR is lower than that of the frequentist VAR. Moreover, the results show that the forecast made using the BVAR is more precise than the forecast made using random walk model for the CPI and using white noise model for the interbank rate. However, the BVAR cannot beat the random walk while forecasting the industrial production index.
Smoking is a problem, bringing signifi cant social and economic costs to Russiansociety. However, ratifi cation of the World health organization Framework conventionon tobacco control makes it possible to improve Russian legislation accordingto the international standards. So, I describe some measures that should be taken bythe Russian authorities in the nearest future, and I examine their effi ciency. By studyingthe international evidence I analyze the impact of the smoke-free areas, advertisementand sponsorship bans, tax increases, etc. on the prevalence of smoking, cigaretteconsumption and some other indicators. I also investigate the obstacles confrontingthe Russian authorities when they introduce new policy measures and the public attitudetowards these measures. I conclude that there is a number of easy-to-implementanti-smoking activities that need no fi nancial resources but only a political will.
One of the most important indicators of company's success is the increase of its value. The article investigates traditional methods of company's value assessment and the evidence that the application of these methods is incorrect in the new stage of economy. So it is necessary to create a new method of valuation based on the new main sources of company's success that is its intellectual capital.