Minnesota-type adaptive hierarchical priors for large Bayesian VARs

Large Bayesian VARs with stochastic volatility are increasingly used in empirical macroeconomics. The key to making these highly parameterized VARs useful is the use of shrinkage priors. We develop a family of priors that captures the best features of two prominent classes of shrinkage priors: adaptive hierarchical priors and Minnesota priors. Like adaptive hierarchical priors, these new priors ensure that only ‘small’ coefficients are strongly shrunk to zero, while ‘large’ coefficients remain intact. At the same time, these new priors can also incorporate many useful features of the Minnesota priors such as cross-variable shrinkage and shrinking coefficients on higher lags more aggressively. We introduce a fast posterior sampler to estimate BVARs with this family of priors—for a BVAR with 25 variables and 4 lags, obtaining 10,000 posterior draws takes about 3 min on a standard desktop computer. In a forecasting exercise, we show that these new priors outperform both adaptive hierarchical priors and Minnesota priors.     

Forecasting U.S. money growth using economic uncertainty measures and regularisation techniques

This paper examines the out-of-sample forecasting properties of six different economic uncertainty variables for the growth of the real M2 and real M4 Divisia money series for the U.S. using monthly data. The core contention is that information on economic uncertainty improves the forecasting accuracy. We estimate vector autoregressive models using the iterated rolling-window forecasting scheme, in combination with modern regularisation techniques from the field of machine learning. Applying the Hansen-Lunde-Nason model confidence set approach under two different loss functions reveals strong evidence that uncertainty variables that are related to financial markets, the state of the macroeconomy or economic policy provide additional informational content when forecasting monetary dynamics. The use of regularisation techniques improves the forecast accuracy substantially.     

Correction to: Optimal and robust combination of forecasts via constrained optimization and shrinkage

We provide a correction to Proposition 1 in Optimal and robust combination of forecasts via constrained optimization and shrinkage, published in the International Journal of Forecasting 38(1):97-116 (2021). This correction has no impact on any other result (neither theoretical nor empirical) provided in the above paper.     

Empirical evidence on individual, group and shrinkage seasonal indices

This paper provides empirical evidence on forecasting seasonal demand using both individual and group seasonal indices methods. The findings show that the group seasonal indices methods outperform the individual seasonal indices method. This paper also offers empirical results from comparing two shrinkage methods with the group seasonal indices methods. The theoretical rules developed by the authors for choosing between group seasonal indices and individual seasonal indices produce more accurate forecasts than do published rules for choosing between shrinkage methods, when measured by the MSE, and are competitive when measured by the symmetric MAPE.     

Shrinkage estimation of semiparametric multiplicative error models

Within models for nonnegative time series, it is common to encounter deterministic components (trends, seasonalities) which can be specified in a flexible form. This work proposes the use of shrinkage type estimation for the parameters of such components. The amount of smoothing to be imposed on the estimates can be chosen using different methodologies: Cross-Validation for dependent data or the recently proposed Focused Information Criterion. We illustrate such a methodology using a semiparametric autoregressive conditional duration model that decomposes the conditional expectations of durations into their dynamic (parametric) and diurnal (flexible) components. We use a shrinkage estimator that jointly estimates the parameters of the two components and controls the smoothness of the estimated flexible component. The results show that, from the forecasting perspective, an appropriate shrinkage strategy can significantly improve on the baseline maximum likelihood estimation.     

Forecasting Foreign Exchange Markets Using Google Trends: Prediction Performance of Competing Models

Abstract

Foreign exchange markets affect a variety of humans and businesses worldwide and there is a wide array of literature aimed at providing more accurate forecasts of their movement. In an attempt to quantify human expectations, Google query search terms related to foreign exchange markets are used to help explain and predict foreign exchange rates between the United States’ dollar and ten other currencies during the time period of January 2004 and August 2018. We find evidence that, while Google Trends can be helpful in prediction, it is necessary to implement some sort of shrinkage or sparsity scheme on the coefficients.     

Machine learning for regularized survey forecast combination: Partially-egalitarian LASSO and its derivatives

Despite the clear success of forecast combination in many economic environments, several important issues remain incompletely resolved. The issues relate to the selection of the set of forecasts to combine, and whether some form of additional regularization (e.g., shrinkage) is desirable. Against this background, and also considering the frequently-found good performance of simple-average combinations, we propose a LASSO-based procedure that sets some combining weights to zero and shrinks the survivors toward equality (“partially-egalitarian LASSO”). Ex post analysis reveals that the optimal solution has a very simple form: the vast majority of forecasters should be discarded, and the remainder should be averaged. We therefore propose and explore direct subset-averaging procedures that are motivated by the structure of partially-egalitarian LASSO and the lessons learned, which, unlike LASSO, do not require the choice of a tuning parameter. Intriguingly, in an application to the European Central Bank Survey of Professional Forecasters, our procedures outperform simple average and median forecasts; indeed, they perform approximately as well as the ex post best forecaster.     

Long-term wealth growth portfolio allocation under parameter uncertainty: A non-conservative robust approach

The Kelly portfolio, which is documented to have the highest wealth growth rate of any other portfolio in the long run, has highly risky and unstable performance in the short term. This paper offers a hybrid approach to address this problem by integrating the concept of ridge regression and shrinkage estimation into a robustly modified Kelly portfolio. The proposed approach is a two-stage optimization process that not only takes into account the effect of estimation error but also solves the notoriously conservative problem introduced by the robust optimization method. By extending the worst-case scenarios considered by the robust Kelly portfolio, our approach significantly improves its out-of-sample performance without compromising risk reduction. In an extensive out-of-sample analysis with simulated and empirical data sets, we also characterize the impacts of the robustness level and the length of the rolling window on the final result. Moreover, we conduct a comparative study to confirm the validity of the proposed approach, and our model allows the investor to have a better risk-return trade-off than other traditional models.