베이지언VAR 모형의 최적 초모수 추정을 이용한 전망 (Forecasting with the Optimal Choice of Hyperparameters for Bayesian VARs)

서지정보

· 발행기관 : 한국금융학회
· 수록지 정보 : 금융연구 / 38권 / 3호 / 71 ~ 99페이지
· 저자명 : 성병희

초록

베이지언 VAR모형은 대형 거시전망모형과 다른 전망모형에 필적하는 성과를 나타내는 것으로 알려져 국내 많은 연구소와 기관에서 활용하고 있다. 그동안 모형 활용 경험에서 비추어 보면 베이지언 VAR모형의 전망에서 유의하였던 부문은 예측오차가 가장 작은 초모수를 선택하는 것이었다. 본 논문에서는 초모수를 추정되어야 할 또 하나의 모수로 간주하고 자료에 기반하여 추정하는 방법론을 활용하여 초모수를 추정한 후 이를 바탕으로 표본외전망을 실시하였다. 기존 예측오차가 가장 작은 초모수를 선택하고 이를 일정기간 동안 고정하여 전망에 이용하는 방식과 새로운 방식간 전망성과 측면에서 차이가 나는지 살펴보았다. 최근 국내은행의 치열한 경쟁의 대상인 중소기업대출을 전망하는 모형을 구축하였는데 전망시계에 따라 추가된 자료에 근거하여 매번 초모수를 추정하는 전망이 기존 고정 초모수 전망에 비해 전망성과가 개선되는 것으로 나타났다. 한편 그 과정에서 추정된 초모수가 시간이 지나면서 고정되어 있지 않고 변화하였으며 일부 초모수의 경우 그 변화 정도가 코로나19를 거치면서 시계열간 상호관계가 변화했을 가능성을 시사할 정도로 큰 것으로 확인할 수 있었다. 아울러 조건부전망을 이용하여 코로나 때 실시되었던 금융권의 대출 만기 연장과 원리금 상환유예 프로그램 등이 금리인하 정책효과 못지않게 중기대출 증가에 크게 기여한 것으로 나타났다.

영어초록

The Bayesian VAR model has demonstrated performance on par with large-scale macroeconomic forecasting models and other predictive models, which has led to its widespread adoption among various domestic research institutes and organizations. The practitioner's application experience of the model has highlighted the importance of selecting hyperparameters that minimize forecast errors. This study treats hyperparameters as parameters to be estimated from the data, utilizing a methodology that estimates these hyperparameters and then conducts out-of-sample forecasts based on the estimates.
The study compares the forecasting performance of this new methodology against the existing approach of keeping hyperparameters constant that previously minimized prediction errors. Specifically, a forecasting model for small and medium enterprises(hereinafter, SMEs) loans—a highly competitive area for domestic banks—was developed. Using data from 2004 to 2013, we conducted a forecast for 2014 (four quarters) and calculated the forecast error. Subsequently, we compared the mean squared error (percentage) of the SMEs loans forecasts from 2014 to 2023, using a recursive estimation method. The models used for the forecasts generally showed a prediction error within the acceptable range of 5.0%, indicating their accuracy as forecasting models. The prediction error was slightly smaller when estimating optimal hyperparameters than when using a method that keeps hyperparameters fixed for an extended period. The results indicated that forecasts based on re-estimating hyperparameters with updated data appeared to outperform those based on fixed hyperparameters.
Additionally, to observe the trend of the estimated hyperparameters, we examined the quarterly estimates (41 times) from the fourth quarter of 2013 to the fourth quarter of 2023 for the hyperparameters used in the forecasts over the past ten years. It was observed that the estimated hyperparameters varied over time, showing significant changes during the COVID-19 pandemic period. Furthermore, to examine the presence and possibility of structural changes, we used the methodology of Bai, Jushan, and Pierre Perron (2003) and checked the structural change points through the Quandt Likelihood Ratio test statistic. The presence of structural changes of the hyperparameter λ, which controls the overall tightness of the model, was found to be statistically significant at the 10% level. The case of hyperparameter SUR, related to the prior distribution of the sum of coefficients considering data with stochastic trends (unit roots), was statistically significant at the 5% level. The case of hyperparameter SOC, which controls the prior distribution of the initial dummy observations allowing for co-integration relationships in the data, was statistically significant at the 1% level. The timing of structural change was the fourth quarter of 2020, the first quarter of 2020, and the fourth quarter of 2019, respectively. It suggests potential shifts in the time-series relationships among variables around 2020.
Moreover, conditional forecasts revealed that financial measures implemented during the pandemic, such as loan maturity extensions and repayment deferral programs, significantly contributed to the increase in SMEs loans, comparable to the effects of interest rate reduction policies. The policy effects were compared from the first quarter of 2000 to the third quarter of 2021, the period when the Bank of Korea lowered interest rates. The effect of the interest rate cuts on the growth rate of small and medium-sized business loans was estimated at 1.6%p on a quarterly average, while the effect of the COVID-19 financial response measures was estimated at 2.0%p. This suggests that the impact of the COVID-19 financial response measures was as significant as the effect of the interest rate cuts.

참고자료

· 없음