Addressing COVID-19 Outliers in BVARs with Stochastic Volatility

Abstract

Incoming data in 2020 posed sizable challenges for the use of VARs in economic analysis: Enormous movements in a number of series have had strong effects on parameters and forecasts constructed with standard VAR methods. We propose the use of VAR models with time-varying volatility that include a treatment of the COVID extremes as outlier observations. Typical VARs with time-varying volatility assume changes in uncertainty to be highly persistent. Instead, we adopt an outlier-adjusted stochastic volatility (SV) model for VAR residuals that combines transitory and persistent changes in volatility. In addition, we consider the treatment of outliers as missing data. Evaluating forecast performance over the last few decades in quasi-real time, we find that the outlier-augmented SV scheme does at least as well as a conventional SV model, while both outperform standard homoskedastic VARs. Point forecasts made in 2020 from heteroskedastic VARs are much less sensitive to outliers in the data, and the outlier-adjusted SV model generates more reasonable gauges of forecast uncertainty than a standard SV model. At least pre-COVID, a close alternative to the outlier-adjusted model is an SV model with t-distributed shocks. Treating outliers as missing data also generates better-behaved forecasts than the conventional SV model. However, since uncertainty about the incidence of outliers is ignored in that approach, it leads to strikingly tight predictive densities.

Censored Density Forecasts: Production and Evaluation

“…Censored density forecasts assume that the probabilities in the outer tails are unknown and may well be drawn from a different (unknown) distribution to the inner region of the density specified parametrically. Like recent work that has allowed for outliers when modeling the macroeconomy in response to the COVID-19 shock (for example, see Carriero et al (2021)), censored density forecasts require an assumption about how often outliers occur. But they have the relative attraction of not requiring an assumption about what density any outliers are then drawn from.…”

“…Our approach thus offers an alternative to model-based methods such as Carriero et al (2021), who, when modeling and forecasting macroeconomic data, downweight extreme observations, such as those observed during the COVID-19 pandemic, by allowing for both persistent and temporary heteroscedasticity.…”

Forecasting with Shadow-Rate VARs

“…At the one-step-ahead horizon, the odds of the nominal interest rate rising above the ELB are 50 percent (and increasing for longer horizons). 12 The resulting tendency to expect an imminent departure from the ELB contrasts with the shadow-rate VAR that is described next. In the basic version of the shadow-rate approach, the VAR vector includes the shadow rate, s t , instead of the actual interest rate, i t , and with s t < ELB, predictions of future interest rates will need to see projections of s t rise above the ELB to expect the same for i t .…”

“…In companion work we investigate the use of outlier-adjusted versions of the SV model to handle the particular swings in data seen since the outbreak of COVID-19(Carriero, et al, 2021). Through the use of latent states to capture outliers, the outlier-adjusted procedures discussed there retain a conditionally Gaussian representation, and combination with the shadow-rate sampling methods described here is straightforward.…”

Tail Forecasting with Multivariate Bayesian Additive Regression Trees

“…During a pandemic, this high persistence in the volatility process could be detrimental for predictive accuracy, since the predictive variance only slowly adjusts to new information. As a solution, Carriero, et al (2021) discuss several alternative volatility models that allow for combining transitory and persistent changes in the volatility. These models allow for richer volatility dynamics but also assume a parametric and known law of motion.…”