We develop a vector autoregressive model with time variation in the mean and the variance. The unobserved time-varying mean is assumed to follow a random walk and we also link it to long-term Consensus forecasts, similar in spirit to so called democratic priors. The changes in variance are modelled via stochastic volatility. The proposed Gibbs sampler allows the researcher to use a large cross-sectional dimension in a feasible amount of computational time. The slowly changing mean can account for a number of secular developments such as changing inflation expectations, slowing productivity growth or demographics. We show the good forecasting performance of the model relative to popular alternatives, including standard Bayesian VARs with Minnesota priors, VARs with democratic priors and standard time-varying parameter VARs for the euro area, the United States and Japan. In particular, incorporating survey forecast information helps to reduce the uncertainty about the unconditional mean and along with the time variation improves the long-run forecasting performance of the VAR models.
We study optimality properties in finite samples for time-varying volatility models driven by the score of the predictive likelihood function. Available optimality results for this class of models suffer from two drawbacks. First, they are only asymptotically valid when evaluated at the pseudo-true parameter. Second, they only provide an optimality result 'on average' and do not provide conditions under which such optimality prevails. We show in a finite sample setting that score-driven volatility models have optimality properties when they matter most. Score-driven models perform best when the data is fattailed and robustness is important. Moreover, they perform better when filtered volatilities differ most across alternative models, such as in periods of financial distress. These results are confirmed by an empirical application based on U.S. stock returns.
We investigate covariance matrix estimation in vast-dimensional spaces of 1,500 up to 2,000 stocks using fundamental factor models (FFMs). FFMs are the typical benchmark in the asset management industry and depart from the usual statistical factor models and the factor models with observed factors used in the statistical and finance literature. Little is known about estimation risk in FFMs in high dimensions. We investigate whether recent linear and non-linear shrinkage methods help to reduce the estimation risk in the asset return covariance matrix. Our findings indicate that modest improvements are possible using high-dimensional shrinkage techniques. The gains, however, are not realized using standard plug-in shrinkage parameters from the literature, but require sample dependent tuning.
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