Three Essays in Modeling and Forecasting Economic Dynamics Público

Liu, Xiaochun (2014)

Permanent URL: https://etd.library.emory.edu/concern/etds/x920fx47g?locale=es
Published

Abstract

An important problem of modern financial economics is to understand and quantify the interaction between macroeconomics and financial markets under hypothetically distress scenarios. Modeling economic dynamics given a hypothetically distress economic scenario requires knowledge and techniques for extreme values or events. In this dissertation, on the econometrics side, I propose new econometric approaches for modeling evolutionary processes in tails of a data distribution, and constructing decomposition models to forecast excess stock returns by considering the role of dynamic higher moments, such as time-varying skewness. On the financial economics side, my research analyzes the counter-cyclical risk pattern of stock markets, asymmetric dynamics in macroeconomic variables, and systemic risk measure of financial institutions subject to regime switching in tails. The first essay proposes a new time-series econometric model to estimate quantiles of a data distribution subject to regime shifts, so-called Markov-Switching Quantile Autoregression (MSQAR). The purpose of this new econometric model is to characterize nonstationary natures of different parts of a data distribution. This is achieved via the assumption that quantile error terms follow a three-parameter asymmetric Laplace distribution. To deal with the difficulty in model estimation, I adopt a "block-at-a-time" Metropolis-Hastings sampling. The second essay applies the proposed MSQAR approach to stress-testing the U.S largest commercial banks by measuring systemic risk of individual banks subject to economic regime shifts. The new systemic risk measures show that the benchmark model of CoVaR approach underestimates systemic risk contributions of individual banks by around 131 basis points of asset loss on average. In addition, Banking Systemic Risk Index is constructed by value-weighted individual contributions. The third essay proposes a new approach to modeling time-varying skewness, the model performance of which is evaluated in out-of-sample forecast of the U.S. excess stock returns in terms of both statistical significance and economic values. Interestingly, a forecast combination, more robust to structural instability than the individual forecasts, performs significantly better out-of-sample than the benchmarks. The skewness timing of the proposed time-varying dependence models yields an average gain in the returns around 195 basis points per year over the forecast sample period.

Table of Contents

Contents

List of Tables

List of Figures

Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 1. Markov-Switching Quantile Autoregression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2. Asymmetric Laplace Distribution Connection . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 9

1.3. Markov-Switching Quantile Autoregression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4. Bayesian Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.5. Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . 19

1.6. Empirical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . 22

1.6.1. Stock Market Risk . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . 23

1.6.2. Asymmetric Persistence in Macroeconomic Dynamics .. . . . . . . . . . . . . . .. . . . . . . 26

1.6.3. Quantile Monotonicity . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . 28

1.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 29

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Chapter 2. Systemic Risk of Commercial Banks with Regime Switching in Tails . . . . . . . . . 49

2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. . . . . . . . . . 50

2.2. Systemic Risk Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.2.1. CoVaR . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 55

2.2.2. Markov-Switching CoVaR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.2.3. Markov-Switching CoES . . . . . . . . . . . . . . . . . . . . . .. . .. . . . . . . .. . . . . . . . .. . . . . . . 61

2.3. Stress-testing Commercial Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2.3.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2.3.2. Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

2.3.3. Banking Systemic Risk Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 70

2.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Chapter 3. Modeling Time-Varying Skewness via Decomposition for Out-of-Sample Forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.2. The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.2.1. Joint Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 88

3.2.2. Dynamic Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

3.2.3. Likelihood Function . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 93

3.2.4. Forecasting Methods . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . 94

3.3. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

3.4. Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 97

3.4.1. Density Forecasts of Copula Specications . . . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . . . 98

3.4.2. Statistical Signicance of Out-of-Sample Forecasts . . . . . . . . .. . . . . . . . . . . . . . . . . . 99

3.4.3. Economic Values of Out-of-Sample Forecasts . . . . . . . . . . . . . . .. . . . . . . . . . . . . 104

3.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . 120

Appendix A. Marginals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

List of Tables

1.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 30

1.2 Summary Statistics for the Predictability of Simulated Regimes. . . . . . . . . . . . . . . . . . . . . . 33

1.3 Data Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .. . . . . . . . . 33

1.4 Estimation Results for S&P 500 Index Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.5 Estimation Results for Macroeconomic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.6 Real GDP Growth Rates: Predictability of Regime 2 . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 36

2.1 The Sample List of the U.S. Largest Commercial Banks as of 06/30/2012 Ranked in Total

Assets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

2.2 MSQAR model estimation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

2.3 VaR, MSVaR and MSES estimates of individual banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

2.4 Systemic risk sensitivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

2.5 Systemic Risk Contribution of each bank to financial system . . . . . . . . . . . . . . . . . . . . . . . 76

2.6 Correlation matrix of banks' systemic risk contributions measured by MSCoV aR1 . . . . . 77

3.1 Pretesting the U.S. Excess Stock Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

3.2 In-Sample Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

3.3 Density Forecast Comparisons of Copula Specifications . . . . . . . . . . . . . . . . . . . . . . .. . . 111

3.4 Out-of-Sample Forecast Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

3.5 Tests of Conditional Predictive Ability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

3.6 Sources of Forecasting Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 114

3.7 Forecast Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . 115

3.8 Economic Values of Market Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

3.9 Economic Values of Volatility and Skewness Timings . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

List of Figures

1.1 Posteriors of the Parameter Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 37

1.2 Time Series Data Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

1.3 Quantile Parameter Estimation: S&P 500 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

1.4 Smoothed Transition Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 40

1.5 The Estimated Quantiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 41

1.6 Quantile Parameter Estimations for Macroeconomic Variables . . . . . . . . . . . . . . . . . . . . . 42

1.7 Smoothed Transition Probability for Real GDP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

1.8 Quantile Monotonicity for each regime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.1 MSES for a subset of the sample banks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

2.2 Systemic risk contributions for a subset of the sample banks: MSCoV aR1 vs CoV aR . . .79

2.3 Banking Systemic Risk Index (BSRI). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.1 Out-of-Sample Estimators of Dependency Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

3.2 Fluctuation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 119

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