Machine Learning in the Growth-at-Risk Context. A Comparison of Predictors

Table of Contents

1 Introduction

2 The Concept of Growth-at-Risk

2.1 Literature Overview

2.2 Quantile Regression

2.3 LASSO Quantile Methods

2.3.1 LASSO Quantile Regression

2.3.2 Relaxed LASSO Quantile Regression

2.3.3 Adaptive LASSO Quantile Regression

2.3.4 Elastic Net Quantile Regression

2.4 Backtesting

3 Empirical Analysis

3.1 Data

3.2 In-Sample Analysis

3.3 Out-of-Sample Analysis

3.3.1 Expanding Window Results

3.3.2 Rolling Window Results

3.3.3 Variable Selection in Out-of-Sample Analysis

3.4 Discussion

4 Conclusion

Objectives and Research Focus

The primary objective of this thesis is to enhance the predictive power of Growth-at-Risk (GaR) models by applying machine learning-based variable selection techniques. The work centers on evaluating whether penalized quantile regression methods, such as LASSO and its variants, can outperform the benchmark model formulated by Adrian et al. (2019), which relies on aggregate indicators of financial conditions.

• Comparison of machine learning-based variable selection methods in the GaR context.
• Evaluation of LASSO, Relaxed LASSO, Adaptive LASSO, and Elastic Net quantile regressions.
• Backtesting performance analysis using expanding and rolling window approaches.
• Investigation of variable selection patterns across different quantiles and time horizons.

Excerpt from the Book

Summary of Chapters

1 Introduction: Provides the context of the Global Financial Crisis and introduces the Growth-at-Risk (GaR) concept, highlighting the need for advanced variable selection in predicting economic downturns.

2 The Concept of Growth-at-Risk: Formally introduces the GaR framework, outlines quantile regression methodology, and details various penalized methods, including LASSO, Relaxed LASSO, Adaptive LASSO, and Elastic Net, while discussing backtesting.

3 Empirical Analysis: Conducts an analysis on US data (1986-2019) using various models, evaluating them against the benchmark through in-sample and out-of-sample tests, and discussing the variable selection results.

4 Conclusion: Synthesizes the findings, noting that while penalized methods provide insights, the benchmark often performs strongly in specific extreme downside quantiles, and emphasizes the conditional applicability of the proposed models.

Keywords

Growth-at-Risk, GaR, Quantile Regression, Machine Learning, LASSO, Adaptive LASSO, Elastic Net, Variable Selection, Backtesting, GDP growth, Financial instability, Forecasting, Predictive power, Macrofinance, Econometrics

Frequently Asked Questions

What is the core focus of this Master Thesis?

The thesis focuses on improving the predictive accuracy of Growth-at-Risk (GaR) models by replacing aggregate index-based approaches with machine learning-based variable selection methods that automatically identify relevant individual economic indicators.

Which specific statistical methods are compared in this work?

The work systematically compares the benchmark Quantile Regression (QR) model against penalized variants: LASSO Quantile Regression, Relaxed LASSO, Adaptive LASSO, and Elastic Net Quantile Regression.

What is the primary motivation for introducing these machine learning methods?

The primary motivation is to overcome limitations in existing GaR literature, specifically the reliance on aggregate indices like the National Financial Conditions Index (NFCI) and the issue of dealing with a vast number of potential economic predictors.

How is the model performance evaluated?

Model performance is rigorously tested through backtesting protocols using both expanding and rolling forecasting windows, with evaluation metrics including empirical coverage, average prediction length, and tick loss.

Does the machine learning approach lead to superior results?

The results show mixed performance; while penalized models often show improved results in specific periods (e.g., during the Global Financial Crisis) or for higher quantiles, the benchmark QR model remains highly competitive for the most extreme downside risks.

What role does the Global Financial Crisis play in the analysis?

The thesis uses the period surrounding the 2008 crisis to explicitly analyze how well the different models capture major economic shocks and subsequent recoveries, highlighting specific strengths and weaknesses of the proposed penalized methods compared to the benchmark.

Which variables were identified as most relevant for GaR prediction?

The empirical findings highlight that variables such as house prices, corporate debt-to-GDP, and crude oil prices are frequently selected as significant indicators for lower downside quantiles in the US data.

Are there limitations to the interpretation of the coefficients in these models?

Yes, due to the shrinkage nature of LASSO-based methods, the thesis notes that economic interpretability should be handled with caution, as the primary goal is primarily focused on accurate out-of-sample prediction.