韩国央行利用风险增长密度预测改进韩国GDP增长平均预测（英）

Using Density Forecast for Growth-at-Risk to Improve Mean Forecast of GDP Growth in Korea

Introduction

The Bank of Korea (BOK) is exploring the use of density forecasts to enhance the accuracy of point forecasts for Korean GDP growth rates. This study focuses on the period from 2013:Q3 to 2022:Q1. Density forecasts are used to improve point forecasts, but combining them does not yield significant improvements.

Key Findings

1. Improvement in Point Forecasts:

   • Density forecasts improve point forecasts when effectively approximated and represented as finite-dimensional vectors.
   • Using leading functional principal components (FPc) as the basis for approximation, the precision of point forecasts for Korean GDP growth rates improves significantly.
   • The mean squared error (MSE) of point forecasts decreases by more than 33% after adjusting with density forecasts using the FPc basis.

2. Functional Regression:

   • A functional regression of future GDP growth rates on their density forecast and point forecast is employed.
   • The functional regression helps in directly addressing whether density forecasts provide useful information for point forecasts and how to combine additional information from density forecasts with point forecasts.

3. Constructing Key Variables:

   • The Financial Condition Index (FCI) is constructed using various economic variables reflecting macro and financial market conditions in Korea.
   • Covariates include the real GDP gap, the U.S. federal funds rate (FFR), the spread between the U.S. FFR and the Korean call rate, and the FCI.

4. Empirical Results:

   • Four conditional quantile values (5%, 25%, 75%, 95%) of GDP growth rates are computed conditionally on the set of covariates.
   • A skewed t-density with four parameters is defined as the density forecast that most closely matches the computed conditional quantiles.

Methodology

• Density Forecast Representation: The density forecast is converted into a finite-dimensional vector using an appropriately chosen functional basis (FPc).
• Functional Regression: The regression model uses both the density forecast and the point forecast as covariates.

Conclusion

• The study finds that density forecasts can significantly improve the precision of point forecasts for Korean GDP growth rates when effectively represented and combined with point forecasts through functional regression.
• The use of FPc as the functional basis enhances the accuracy of point forecasts, reducing the MSE by more than 33%.

Keywords

• GDP growth rate
• Point forecast
• Growth-at-Risk density forecast
• Functional regression
• Functional basis
• Functional principal component analysis

JEL Classification

• C53
• E17
• E37