Hierarchical Shrinkage in Time-Varying Parameter Models

Abstract

In this paper, we forecast EU-area inflation with many predictors using time-varying parameter models. The facts that time-varying parameter models are parameter-rich and the time span of our data is relatively short motivate a desire for shrinkage. In constant coefficient regression models, the Bayesian Lasso is gaining increasing popularity as an effective tool for achieving such shrinkage. In this paper, we develop econometric methods for using the Bayesian Lasso with time-varying parameter models. Our approach allows for the coefficient on each predictor to be: i) time varying, ii) constant over time or iii) shrunk to zero. The econometric methodology decides automatically which category each coefficient belongs in. Our empirical results indicate the benefits of such an approach.

Can the Sharia-based Islamic stock market returns be forecasted using large number of predictors and models?

“…The time-varying parameter approach has the advantage to allow the parameters to change over time, but may have a poor out-of sample performance in the presence of large sets of predictors. Hence, we use the Bayesian shrinkage based on the least absolute shrinkage selection operator (LASSO) (Belmonte et al, 2013), the dynamic model averaging (DMA) and the dynamic model selection (DMS) (Koop and Korobilis, 2012). In particular, the DMA combines information from a set of predictors by averaging forecast across a set of equations, while the DMS involves selecting the single model with the highest predictive power and using this to forecast.…”

“…-Mean: Average of individual forecast at date t; -Median: Median of individual forecast at date t; -Trimmed mean: Trimmed mean of individual forecast at date t, 5 percent symmetric trimming; -DMSFE (delta): Combined forecast where the Discount Mean Square Forecast Error criterion is used to determine the weights of the individual forecast at date t; delta being the discount factor; -C (K, PB): Cluster combining method forecast with K the number of clusters; -PC (IC_P3): Forecasts from regression onto principal components of the panel of forecasts; number of principal components determined by IC_P3 information criteria proposed by Bai and Ng (2002); -A 60 month holding period is used for the DMSFE and cluster combination methods; -BA refers to the Bootstrap Aggregating, popularly known as bagging model; -Factor model: 3 factors (chosen based on the IC_P3) used together in equation (1) and λ is the forgetting factor for the state equation for the parameter; -BMA: Specific form of DMA limited to static models with parameter uncertainty; -DMS: Dynamic Model Selection; and -The reader is referred to Belmonte et al (2013) and Koop and Koroboris (2012) for further details on the time-varying models.…”

Data-Based Priors for Vector Autoregressions with Drifting Coefficients

“…Based on a simple reparametrization for state-space models (e.g. Frühwirth-Schnatter and Wagner, 2010; Belmonte, Koop and Korobilis, 2014) we show that we can develop simple prior structures which add minimal computational complexity to the standard TVP-VAR estimation algorithm used in the macroeconomic literature (e.g. the popular algorithm used in Primiceri, 2005).…”

“…While such simplification makes prior selection easier and more convenient (only a single hyperparameter to select), there is a "downside risk" of following this approach in the flexible class of TVP-VAR models, since posterior quantities applied economists usually report (e.g. forecasts, impulse responses) can become very sensitive to selection of this hyperparameter 1 .…”

On efficient Bayesian inference for models with stochastic volatility

“…This leads to samples from an approximate posterior distribution for the parameters of the SV More recently, the KSC sampler has been applied to more complicated mod-els. For example, Belmonte et al (2013) consider dynamic regression models with stochastic volatility…”