Browsing by Author "Patton, Andrew J"

The dissertation consists of four chapters that concern topics on copulas for high dimensions. Chapter 1 proposes a new general model for high dimension joint distributions of asset returns that utilizes high frequency data and copulas. The dependence between returns is decomposed into linear and nonlinear components, which enables the use of high frequency data to accurately measure and forecast linear dependence, and the use of a new class of copulas designed to capture nonlinear dependence among the resulting linearly uncorrelated residuals. Estimation of the new class of copulas is conducted using a composite likelihood, making the model feasible even for hundreds of variables. A realistic simulation study verifies that multistage estimation with composite likelihood results in small loss in efficiency and large gain in computation speed.

Chapter 2, which is co-authored with Professor Andrew Patton, presents new models for the dependence structure, or copula, of economic variables based on a factor structure. The proposed models are particularly attractive for high dimensional applications, involving fifty or more variables. This class of models generally lacks a closed-form density, but analytical results for the implied tail dependence can be obtained using extreme value theory, and estimation via a simulation-based method using rank statistics is simple and fast. We study the finite-sample properties of the estimation method for applications involving up to 100 variables, and apply the model to daily returns on all 100 constituents of the S\&P 100 index. We find significant evidence of tail dependence, heterogeneous dependence, and asymmetric dependence, with dependence being stronger in crashes than in booms.

Chapter 3, which is co-authored with Professor Andrew Patton, considers the estimation of the parameters of a copula via a simulated method of moments type approach. This approach is attractive when the likelihood of the copula model is not known in closed form, or when the researcher has a set of dependence measures or other functionals of the copula that are of particular interest. The proposed approach naturally also nests method of moments and generalized method of moments estimators. Drawing on results for simulation based estimation and on recent work in empirical copula process theory, we show the consistency and asymptotic normality of the proposed estimator, and obtain a simple test of over-identifying restrictions as a goodness-of-fit test. The results apply to both $iid$ and time series data. We analyze the finite-sample behavior of these estimators in an extensive simulation study.

Chapter 4, which is co-authored with Professor Andrew Patton, proposes a new class of copula-based dynamic models for high dimension conditional distributions, facilitating the estimation of a wide variety of measures of systemic risk. Our proposed models draw on successful ideas from the literature on modelling high dimension covariance matrices and on recent work on models for general time-varying distributions. Our use of copula-based models enable the estimation of the joint model in stages, greatly reducing the computational burden. We use the proposed new models to study a collection of daily credit default swap (CDS) spreads on 100 U.S. firms over the period 2006 to 2012. We find that while the probability of distress for individual firms has greatly reduced since the financial crisis of 2008-09, the joint probability of distress (a measure of systemic risk) is substantially higher now than in the pre-crisis period.

This dissertation presents the construction procedure of “high-frequency” daily measure of changes in housing valuations, and analyzes its return dynamics, as well as investigates its relationship to capital markets. The dissertation consists of three chapters. The first chapter introduces the house price index methodologies and housing transaction data, and reviews the related literature. The second chapter shows the construction and modeling of daily house price indexes and highlights the informational advantage of the daily indexes. The final chapter provides detailed empirical and theoretical investigations of housing index return volatilities.

Chapter 2 discusses the relationship of the housing market with the other markets, such as consumer good market and financial markets. Different housing price indexes and their construction methodologies are introduced, with emphases on the repeat sales model and S&P/Case Shiller Home Price Index. A detailed description of the housing transaction data I use in the dissertation is also provided in this chapter.

Chapter 3 is co-authored with Professor Tim Bollerslev and Professor Andrew Patton. We construct daily house price indexes for ten major U.S. metropolitan areas. Our calculations are based on a comprehensive database of several million residential property transactions and a standard repeat-sales method that closely mimics the procedure used in the construction of the popular monthly Case-Shiller house price indexes. Our new daily house price indexes exhibit dynamic features similar to those of other daily asset prices, with mild autocorrelation and strong conditional heteroskedasticity. The correlations across house price index returns are low at the daily frequency, but rise monotonically with the return horizon, and are commensurate with existing empirical evidence for existing monthly and quarterly house price series. Timely and accurate measures of house prices are important in a variety of applications, and are particularly valuable during times of turbulence, such as the recent housing crisis. To quantify the informational advantage of our daily index, we show that a relatively simple multivariate time series model for the daily house price index returns, explicitly allowing for commonalities across cities and GARCH effects, produces forecasts of monthly house price changes that are superior to various alternative forecast procedures based on lower frequency data.

Chapter 4 investigates the properties of housing index return volatilities. Similar to stock market volatility, housing volatilities are found to respond asymmetrically to negative and positive returns. A direct test of volatility on changes in loan-to-value ratio suggests that the observed volatility asymmetry does not stem from changes in degree of housing financial leverage, but could result from the risk premium carried by housing volatility, which is supported by a consumption-based asset pricing model with housing. Moreover, housing and stock volatilities are found to be positively correlated from a set of predictive regressions based on realized variances of housing and stock markets, in which higher (lower) volatility in one market will be followed by higher (lower) volatility in the other. Finally, housing and stock cross-sectional return dispersions are shown to contain useful information in predicting both within-market and cross-market realized volatilities.

Value-at-Risk (VaR) has been the most prevalent market risk measure in the financial sector. Banks, insurance companies and other financial institutions are required to report their VaR estimates to the regulatory authorities since its introduction to the Basel I Accord in 1996. Acknowledging the theoretical deficiencies of this risk measure, The Basel Committee on Banking Supervision proposed to replace VaR with Expected Shortfall (ES), which overcomes these shortcomings. The practical implementation of this measure is still in process as the literature is lack of simple tools for its estimation and evaluation since by definition, the ES depends on the VaR estimate. This dissertation develops several techniques for estimating and conducting inference on VaR and ES models.

The first chapter, which is a joint paper with Andrew J. Patton, implements a 2-step robust estimation method for estimating the Expected Shortfall. We ease the dependence of the ES estimate from the VaR. To achieve this, in the first step the VaR is estimated by nonparametric methods, which helps us to avoid estimation error in the nuisance process. In the second step, we apply a robust estimation technique which controls for small deviations of the VaR estimates from their theoretically true values. We compare this new method to a 1-step joint estimation when VaR and ES are jointly estimated and to a 2-step non-robust estimation method. We find that with the new 2-step method the estimates are more efficient than applying a non-robust version and it performs better than the joint estimation when we do inference on the ES model parameters.

The second chapter, which is joint with Jia Li, Zhipeng Liao and Andrew J. Patton, proposes a novel nonparametric specification test for VaR models. We translate the specification test to a conditional moment restriction test. We estimate the conditional moment function via nonparametric series regression and test whether it is identically zero. We use a strong Gaussian approximation theory to characterize the asymptotic behavior of our sup-t test. In addition, we propose an i.i.d. bootstrap method which performs better in finite sample than the asymptotic approximation at more extreme quantiles. As an empirical exercise, we test Conditional VaR models of US financial institutions.

The third chapter builds on this idea and implements the test for multiple conditional moment restrictions to test the correct specification of VaR and ES jointly. In addition, we also propose an average-t test, whose theoretical properties rely on the sup-t test. We find that the average-t test outperforms the sup-t test at more extreme confidence levels. As an empirical exercise, we test several location-scale models in S&P500 data for correct specification of ES and VaR.

This dissertation studies applied econometric problems in volatility estimation and CDS pricing. The first chapter studies estimation of loss given default from CDS spreads for U.S. corporates. This paper combines a term structure model of credit default swaps (CDS) with weak-identification robust methods to jointly estimate the probability of default and the loss given default of the underlying firm. The model is not globally identified because it forgoes parametric time series restrictions that have ensured identification in previous studies, but that are also difficult to verify in the data. The empirical results show that informative (small) confidence sets for loss given default are estimated for half of the firm-months in the sample, and most of these do not include the conventional value of 0.60. In addition, risk-neutral default probabilities, and hence risk premia on default probabilities, are underestimated when loss given default is exogenously fixed at the conventional value instead of estimated from the data.

The second chapter, which is joint work with Andrew Patton and Kevin Sheppard, studies the accuracy of a wide variety of estimators of asset price

variation constructed from high-frequency data (so-called "realized measures"), and compare them with a simple "realized variance" (RV) estimator. In total, we consider over 400 different estimators, applied to 11 years of data on 31 different financial assets spanning five asset classes, including equities, equity indices, exchange rates and interest rates. We apply data-based ranking methods to the realized measures and to forecasts based on these measures. When 5-minute RV is taken as the benchmark realized measure, we find little evidence that it is outperformed by any of the other measures. When using inference methods that do not require specifying a benchmark, we find some evidence that more sophisticated realized measures significantly outperform 5-minute RV. In forecasting applications, we find that a low frequency "truncated" RV

outperforms most other realized measures. Overall, we conclude that it is

difficult to significantly beat 5-minute RV for these assets.

This dissertation consists of three essays. In the first essay, I analyze the performance of five different classes of integrated variance estimators when applied to various stocks of differing market capitalization in an attempt to discover the circumstances under which one estimator should be chosen over another. In recent years, there has been an explosion of research on the volatility of stock returns. As high frequency stock price data became more readily available, there have been many proposed estimators of integrated variance which attempt to take advantage of the informational gains of high-frequency data while minimizing any potential biases that arise from sampling at such a fine scale. These estimators rely on various assumptions about the price process which can make them difficult to compare theoretically. I find that across several stocks in different size deciles, the truncation estimator outperforms the other estimators of integrated variance. Furthermore, I find that choosing a truncation parameter of 2-3 standard deviations leads to the most accurate estimates on average.

In the second essay, I estimate latent factor models of liquidity and volatility. Common liquidity and volatility factors are extracted using multiple liquidity and volatility measures. Additionally, latent factors are extracted by aggregating across both liquidity and volatility resulting in what we will call the common ``uncertainty'' factors. This underlying uncertainty factor is correlated with the individual and common liquidity and volatility factors as well as returns. I find that the underlying uncertainty risk factor is significantly priced in the cross section of expected returns, while the risks associated solely with liquidity and volatility are not. These results suggest that the liquidity risk and volatility risk may both proxy for an underlying uncertainty risk which drives the significant results when considering them individually.

The third essay further explores the ``uncertainty'' factor and links it to the macroeconomy with the hope of accurately forecasting real GDP growth, growth in industrial production, and growth in the unemployment rate. I show that shocks to the uncertainty factor have both in- and out-of-sample predictability for real GDP growth as well as growth for both industrial production and unemployment rate. While the uncertainty factor significantly improves forecast performance over an AR(1) model, there is no indication that the forecasts based on our uncertainty factor significantly outperform forecasts based on an aggregate liquidity measure.

The main goal of this work is to explore the effects of time-varying extreme jump tail dependencies in asset markets. Consequently, a lot of attention has been devoted to understand the extremal tail dependencies between of assets. As pointed by Hansen (2013), the estimation of tail risks dependence is a challenging task and their implications in several sectors of the economy are of great importance. One of the principal challenges is to provide a measure systemic risks that is, in principle, statistically tractable and has an economic meaning. Therefore, there is a need of a standardize dependence measures or at least to provide a methodology that can capture the complexity behind global distress in the economy. These measures should be able to explain not only the dynamics of the most recent financial crisis but also the prior events of distress in the world economy, which is the motivation of this paper. In order to explore the tail dependencies I exploit the information embedded in option prices and intra-daily high frequency data.

The first chapter, a co-authored work with Andrew Patton, proposes a new class of dynamic copula models for daily asset returns that exploits information from high frequency (intra-daily) data. We augment the generalized autoregressive score (GAS) model of Creal, et al. (2013) with high frequency measures such as realized correlation to obtain a "GRAS" model. We find that the inclusion of realized measures significantly improves the in-sample fit of dynamic copula models across a range of U.S. equity returns. Moreover, we find that out-of-sample density forecasts from our GRAS models are superior to those from simpler models. Finally, we consider a simple portfolio choice problem to illustrate the economic gains from exploiting high frequency data for modeling dynamic dependence.

In the second chapter using information from option prices I construct two new measures of dependence between assets and industries, the Jump Tail Implied Correlation and the Tail Correlation Risk Premia. The main contribution in this chapter is the construction of a systemic risk factor from daily financial measures using a quantile-regression-based methodology. In this direction, I fill the existing gap between downturns in the financial sector and the real economy. I find that this new index performs well to forecast in-sample and out-of-sample quarterly macroeconomic shocks. In addition, I analyze whether the tail risk of the correlation may be priced. I find that for the S&P500 and its sectors there is an ex ante premium to hedge against systemic risks and changes in the aggregate market correlation. Moreover, I provide evidence that the tails of the implied correlation have remarkable predictive power for future stock market returns.

This dissertation contains my research results on two topics of nancial econometrics.

The rst topic is jump regression where the observation selection procedure can be

viewed as the analogy of dimension reduction for the classical big "P" problem in

statistics to the big "N" problem in nancial econometrics. The second topic is about

estimation and testing of time series models for Value-at-Risk (VaR) and Expected

Shortfall (ES), which is the average return on a risky asset conditional on the return

being below some quantile of its distribution, namely its VaR.

The rst chapter, which is joint work with Jia Li, Viktor Todorov and George

Tauchen, develops an ecient mixed-scale estimator for jump regressions using highfrequency

asset returns. A novel bootstrap procedure is proposed to make inference

about our estimator, which has a non-standard asymptotic distribution that cannot

be made asymptotically pivotal via studentization. The Monte Carlo analysis indicates

good nite-sample performance of the general specication test and condence

intervals based on the bootstrap. When the method is applied to a high-frequency

panel of Dow stock prices together with the market index dened by the S&P 500

index futures over the period 2007{2014, we observe remarkable temporal stability

in the way that stocks react to market jumps.

The second chapter is co-authored with Andrew J. Patton and Johanna F. Ziegel.

We use recent results from statistical decision theory to overcome the problem of

\elicitability" for ES by jointly modelling ES and VaR, and propose new time series

models for these risk measures. Estimation and inference methods are provided for

the proposed models and conrmed via simulation studies to have good nite-sample

properties. We apply these models to daily returns on four international equity

indices, and nd the proposed new ES-VaR models outperform forecasts based on

iv

GARCH or rolling window models.

The third chapter is my single-authored paper which proposes a consistent speci-

cation test of dynamic joint models for VaR and ES. To overcome the intractability

problem of the asymptotic distribution of the test statistics under the null hypothesis,

the subsampling approximation is used to get the asymptotic critical values. A

Monte Carlo study shows that the proposed test has better empirical size and power

performance in nite samples than other existing tests.

This dissertation has five chapters. The first chapter provides an overview of the topic and the dissertation. In the second chapter, which is jointly with Andrew Patton, we design a customized time series to images transformation method that is tailored specifically for volatility. We then apply convolution neural network models on the transformed volatility images and find the forecasting performance is significantly better than both the econometrics and machine learning benchmark models in classification and regression. Moreover, we also demonstrate that the customized time series to images transformation approach performs much better than the standard transformation that is off-the-shelf from the machine learning literature.

In the third chapter, which is also jointly with Andrew Patton, we design machine learning algorithms to flexibly estimate the optimal bespoke weighting schemes for constructing RV measure that is tailored specifically to volatility forecasting applications. We find the bespoke RVs have very different schemes than the equal-weighting scheme in the standard RV estimator, and models using bespoke RVs have significant improvements in forecasting performance. Besides obtaining superior forecasting performance using bespoke RVs, we also open the black box and investigate the sources of forecast gains.

Chapter 4 is jointly with Tim Bollerslev and Andrew Patton, where we combine hierarchical clustering methods with the realized semi-correlation to understand whether there are structural break changes in terms of the relationships among different stocks in the context of Covid-19. We design customized algorithms to detect the optimal number of clusters and structural break, and we find there is indeed a structural break related to the Covid-19 and interesting Covid related clusters emerged after the pandemic. Lastly, we show that by leveraging the realized-semicorrelation implied clusters, one could achieve better risk management objectives.

Chapter 5 concludes.