Empirical Applications of Entropy-based Inference Open Access

Zhu, Yifeng (2016)

Permanent URL: https://etd.library.emory.edu/concern/etds/sx61dm88b?locale=en


In the first chapter, I first propose two types of asymmetry measures which based on the tail distribution of the data instead of just the third moment-skewness for stock returns. With these new measures, greater tail asymmetries imply lower average returns in the cross section. In contrast, the relation between the skewness and the expected return is conditional. Then I discuss the relationship between asymmetries and several benchmark anomalies. Size and liquidity effects only appear among low upside asymmetry stocks, while momentum effect is getting stronger when upside asymmetry is increasing. In the second chapter, we examine the potential effect of naturalization on the U.S. immigrants' earnings. We find the earning gap between naturalized citizens and non-citizens is positive over many years, with a tent shape across the wage distribution. We focus on a normalized metric entropy measure of the gap between distributions, and compare with conventional measures at the mean, median and other quantiles. In addition, we further examine the potential sources of the earning gap, the "wage structure" effect and the "composition" effect. Both of these sources contribute to the gap, but the composition effect, while diminishing somewhat after 2005, accounts for about 3/4 of the gap. The unconditional quantile regression and conditional quantile regressions confirm that naturalized citizens have generally higher wages, although the gap varies for different income groups. In the last chapter, I propose linear and nonparametric models to predict crude oil price. Mainly, my forecast depends on three predictor variables, the change in crude oil inventories, its previous prices and product spread. By employing mean-squared prediction error (MSPE) and stochastic dominance (SD) tests, I find that the prediction result of our nonparametric models is significantly better than the random walk model, while the corresponding linear models' performance is better than the random walk model only for longer horizon forecasts (one to two years). And for the nonparametric model including all three predictors, I document MSPE reduction as high as 62.6% compared to the random walk model and the directional accuracy ratio as high as 77.5% at the two years horizon.

Table of Contents

Preface. 1

1 Stock Return Asymmetry and Anomalies. 7

Abstract. 7

1.1 Introduction. 8

1.2 Asymmetry Measures. 11

1.3 Continuous Data Monte Carlo Simulation. 14

1.4 Empirical Results. 16

1.4.1 Data. 16

1.4.2 Stock Level Results. 18

1.4.3 Portfolio Level Results. 22

1.4.4 Asymmetry Conditional on Sentiment. 23

1.4.5 Asymmetry Conditional on VIX. 25

1.4.6 Asymmetry Conditional on Aggregate Stock Market Liquidity. 26

1.4.7 Asymmetry Conditional on Capital Gains Overhang. 26

1.5 Benchmark Anomalies and Asymmetry. 28

1.5.1 Short Term Asymmetry. 28

1.5.2 Benchmark Anomalies. 30

1.5.3 Benchmark Anomalies and Short Term Asymmetry. 32

1.6 Conclusions. 37

2 The Wage Premium of Naturalized Citizenship. 135

Abstract. 135

2.1 Introduction. 136

2.2 Empirical Methodology. 139

2.2.1 Basic Notation. 139

2.2.2 Decision-Theoretics: Entropy as a Distributional Measure of the Earnings Gap. 139

2.2.3 Stochastic Dominance. 141

2.2.4 Counterfactual Distributions. 142

2.2.5 Decomposition of the Distributional Statistics. 144

2.2.6 Unconditional Quantile Partial Eects (UQPE). 144

2.3 Data. 146

2.4 Empirical Results. 147

2.4.1 Distributional Comparison and Analysis. 147

2.4.2 Counterfactual Analysis. 148

2.4.3 Decomposition of the Gap in Conditional Means and Quantiles. 150

2.4.4 the Unconditional Quantile Partial Eect (UQPE) and the Conditional Quantile Partial Eect (CQPE) of Citizenshi. 150

2.5 Conclusions and Future Work. 151

3 Crude Oil Price Prediction: A Nonparametric Approach. 179

Abstract. 179

3.1 Introduction. 181

3.2 Data and One Month Ahead Predictive Models. 185

3.2.1 Data. 185

3.2.2 Unit Root Test. 187

3.2.3 Predictive Models. 187

3.3 The Predictability and Model Comparison for One Month Ahead. 189

3.4 The Models for Longer Horizon Forecasts. 191

3.5 Robustness Check-Stochastic Dominance. 193

3.6 Conclusions. 196

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