Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors

Clark, Todd E.; McCracken, Michael W.; Mertens, Elmar

doi:10.1162/rest_a_00809

“…Figure 8 also shows how the standard deviation of the 2PN density is very stable over time, in contrast to the temporal changes seen in the uncensored rolling N density. It is this temporal variation that motivates the use of models of time variation in forecast error variances, as in, for example, Clark, McCracken, and Mertens (2020).…”

Section: Tracking the Temporal Evolution Of The Censored Intervalsmentioning

confidence: 99%

Censored Density Forecasts: Production and Evaluation

Mitchell

¹

,

Weale

²

2021

Working Paper (Federal Reserve Bank of Cleveland)

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This paper develops methods for the production and evaluation of censored density forecasts. Censored density forecasts quantify forecast risks in a middle region of the density covering a specified probability, and ignore the magnitude but not the frequency of outlying observations. We propose a new estimator that fits a potentially skewed and fat-tailed density to the inner observations, acknowledging that the outlying observations may be drawn from a different but unknown distribution. We also introduce a new test for calibration of censored density forecasts. An application using historical forecast errors from the Federal Reserve Board and the Monetary Policy Committee at the Bank of England illustrates the utility of censored density forecasts when quantifying forecast risks after shocks such as the global financial crisis and the COVID-19 pandemic.

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“…To identify extreme observations as outliers, we use an ex-ante criterion taken from the literature on dynamic factor models that is based on the distance between a given data point and the time-series median. 12…”

Section: Bvar Modelsmentioning

confidence: 99%

Addressing COVID-19 Outliers in BVARs with Stochastic Volatility

Carriero

¹

,

Clark

²

,

Marcellino

³

et al. 2021

SSRN Journal

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0

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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.

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“…cast errors over time, with potential benefits for the accuracy of density forecasts (Clark, McCracken, and Mertens (2020)). In addition, heteroskedasticity affects the estimation of slope coefficients in each VAR equation (at least in finite samples).…”

Section: Introductionmentioning

confidence: 99%

“…In VAR (or AR) models with higher lag orders, the forecast would not singularly depend on the outlier y t but also preceding values that are not necessarily outliers. Nevertheless, outliers in the "jump-off" data point, y t , may unduly influence the forecast 12. In addition, Section 6 reports results for a model variant where (1) is augmented by additional dummy terms for months during the COVID-19 period.…”

mentioning

confidence: 99%

Addressing COVID-19 Outliers in BVARs with Stochastic Volatility

Carriero

¹

,

Clark

²

,

Marcellino

³

et al. 2021

Working Paper (Federal Reserve Bank of Cleveland)

Self Cite

View full text Add to dashboard Cite

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.

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Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors

Cited by 38 publications

References 51 publications

Censored Density Forecasts: Production and Evaluation

Censored Density Forecasts: Production and Evaluation

Addressing COVID-19 Outliers in BVARs with Stochastic Volatility

Addressing COVID-19 Outliers in BVARs with Stochastic Volatility

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