- Email: [email protected]
Financial Statistics and Risk Management: An Overview
Accepted Manuscript Financial Statistics and Risk Management Rong Chen, Per Mykland, Qiwei Yao PII: DOI: Reference:
S0304-4076(16)30089-6 http://dx.doi.org/10.1016/j.jeconom.2016.05.001 ECONOM 4260
To appear in:
Journal of Econometrics
Please cite this article as: Chen, R., Mykland, P., Yao, Q., Financial Statistics and Risk Management. Journal of Econometrics (2016), http://dx.doi.org/10.1016/j.jeconom.2016.05.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Editorial Financial Statistics and Risk Management This volume represents recent advances in the field of Financial Statistics and Risk Management. The papers, written by a diverse group of leading experts, reflect a wide range of topics which continue to attract substantial efforts across econometrics, empirical finance, statistics and mathematics. Most of the papers were presented at the International Symposium on Financial Engineering and Risk Management (FERM) in June 2014, which was held at the Central University of Finance and Economics in Beijing. FERM is by now established as one of the most important conferences in the field. An important area in financial statistics is high frequency data. Over the last decade, we have seen substantial growth in such data, both in the sense that the frequency of trades and quote-revisions is increasing, and also in that the number of securities which are traded at high frequency is getting larger. High frequency data is important in that it permits estimation of certain financial variables, such as volatility, with high precision. Such data are also related to high frequency trading, the regulation of which is a major current policy discussion. This volume contains four papers that involve high frequency data. A¨ıt-Sahalia and Xiu discuss estimators of the continuous and discontinuous part of the quadratic variation (q.v.) in the presence of noise and under regular sampling. They use this to show that the fraction of q.v. due to these two components remained unaltered during the recent financial crisis. This settles a question which has been much debated. Kim and Wang face the question of how to unify short and long term behavior of processes. It is common practice to use potentially incompatible models for high and low frequency, and Kim and Wang present an elegant unification where the low frequency process is allowed to be a GARCH process. Zhang and Zhu study multivariate maximum and minimum processes to capture extreme behavior of high frequency series, and develop an important econometric methodology based on sparsity. Mykland and Zhang show that pre-averaging and pre-Mestimation generally leads to observable processes that are (contiguous to) a locally Gaussian processes, possibly with jumps. This result can ease future analysis of the properties of high frequency data based estimators. Also, pre-averaging is seen to cause jumps to pulverize, while pre-M-estimation mitigates this problem. Analyzing and modeling high dimensional data and functional data have become increasing important and have attracted significant research interests. Three papers in this volume are in this area. time series.
Liu, Xiao and Chen investigate modeling of functional
They propose a convolutional AR model which is interpretable and easy
to estimate, with solid asymptotic results. Modeling building, validation and prediction 1
procedures are also considered. He and Chen study a testing procedure of super-diagonal structure in high dimensional covariance matrices, a challenging problem. By concentrating on the super-diagonal elements of the covariance matrices (the sum of squares of elements neighboring the diagonal), the proposed test is shown to be more powerful in detecting bandedness, local spatial features or specific parametric structures than the more general testing procedures for covariance matrices. Another paper that is related to high-dimensional covariance matrices is by Fan, Han, Liu and Vickers, in which they propose a robust inference of the risks of large portfolios. The estimators are rank and quantile based to safeguard against model misspecification and heavy tail data. Inference is done with a new bootstrap procedure, with novel theoretical investigations. In the context of financial engineering, Chen, Li, Linton and Lu consider the dynamic portfolio choice problem with multiple conditioning variables. They estimate the optimal choice in a practically implementable nonparametric manner, i.e. to estimate the marginal optimal portfolio for each univariate conditioning variable, and then to construct the joint optimal solution by a weighted average of the marginal solutions. Conrad and Mammen have developed a complete asymptotic theory for qMLE of the GARCH-in-Mean model, which was missing in spite of the popularity of the model in practice. To examine financial extreme co-movements, Asimit, Gerrard, Hou and Peng investigate the properties of the limiting conditional Kendall’s tau and propose a nonparametric estimator for this measure. There are also three papers adapting time series or spatio-temporal models for specific applications. Duan proposes a novel and relatively simple model, the local-momentum AR model, for modeling interesting rate term structure. By forcing global mean-reverting but allowing local momentum preserving or building, this parsimonious model is able to capture observed salient features in interest rate time series. In Davis, Hancock and Yao, the theoretical properties of minimum description length is investigated when it is used for detecting the number and location of structure breaks in nonstationary time series. It has direct applications to identifying crisis and regime changes in economics and financial markets. A class of spatio-temporal models is studies by Dou, Parrella and Yao, which extends popular econometric spatial autoregressive panel data models by allowing the scalar coefficients for each location (or panel) to be different from each other. The extension is convincingly justified by the illustration with the consumer price index dynamics for the EU member states. To overcome the innate endogeneity, they propose a generalized Yule-Walker estimation method which applies the least squares estimation to a Yule-Walker equation. Finally we thank all the authors who contribute their new research results to this issue. We also thank the referees for their invaluable help in improving the quality of this final
2
product, and the liaising co-Editor, Jianqing Fan, for his indispensable guidance and help. We sincerely hope that this special issue will give you at least some part of the joy and the fun that we have had in editing it. Rong Chen1 Rutgers University, USA E-mail address: [email protected] Per Mykland University of Chicago, USA Qiwei Yao London School of Economics and Political Science, UK
1
Corresponding editor
3
S0304-4076(16)30089-6 http://dx.doi.org/10.1016/j.jeconom.2016.05.001 ECONOM 4260
To appear in:
Journal of Econometrics
Please cite this article as: Chen, R., Mykland, P., Yao, Q., Financial Statistics and Risk Management. Journal of Econometrics (2016), http://dx.doi.org/10.1016/j.jeconom.2016.05.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Editorial Financial Statistics and Risk Management This volume represents recent advances in the field of Financial Statistics and Risk Management. The papers, written by a diverse group of leading experts, reflect a wide range of topics which continue to attract substantial efforts across econometrics, empirical finance, statistics and mathematics. Most of the papers were presented at the International Symposium on Financial Engineering and Risk Management (FERM) in June 2014, which was held at the Central University of Finance and Economics in Beijing. FERM is by now established as one of the most important conferences in the field. An important area in financial statistics is high frequency data. Over the last decade, we have seen substantial growth in such data, both in the sense that the frequency of trades and quote-revisions is increasing, and also in that the number of securities which are traded at high frequency is getting larger. High frequency data is important in that it permits estimation of certain financial variables, such as volatility, with high precision. Such data are also related to high frequency trading, the regulation of which is a major current policy discussion. This volume contains four papers that involve high frequency data. A¨ıt-Sahalia and Xiu discuss estimators of the continuous and discontinuous part of the quadratic variation (q.v.) in the presence of noise and under regular sampling. They use this to show that the fraction of q.v. due to these two components remained unaltered during the recent financial crisis. This settles a question which has been much debated. Kim and Wang face the question of how to unify short and long term behavior of processes. It is common practice to use potentially incompatible models for high and low frequency, and Kim and Wang present an elegant unification where the low frequency process is allowed to be a GARCH process. Zhang and Zhu study multivariate maximum and minimum processes to capture extreme behavior of high frequency series, and develop an important econometric methodology based on sparsity. Mykland and Zhang show that pre-averaging and pre-Mestimation generally leads to observable processes that are (contiguous to) a locally Gaussian processes, possibly with jumps. This result can ease future analysis of the properties of high frequency data based estimators. Also, pre-averaging is seen to cause jumps to pulverize, while pre-M-estimation mitigates this problem. Analyzing and modeling high dimensional data and functional data have become increasing important and have attracted significant research interests. Three papers in this volume are in this area. time series.
Liu, Xiao and Chen investigate modeling of functional
They propose a convolutional AR model which is interpretable and easy
to estimate, with solid asymptotic results. Modeling building, validation and prediction 1
procedures are also considered. He and Chen study a testing procedure of super-diagonal structure in high dimensional covariance matrices, a challenging problem. By concentrating on the super-diagonal elements of the covariance matrices (the sum of squares of elements neighboring the diagonal), the proposed test is shown to be more powerful in detecting bandedness, local spatial features or specific parametric structures than the more general testing procedures for covariance matrices. Another paper that is related to high-dimensional covariance matrices is by Fan, Han, Liu and Vickers, in which they propose a robust inference of the risks of large portfolios. The estimators are rank and quantile based to safeguard against model misspecification and heavy tail data. Inference is done with a new bootstrap procedure, with novel theoretical investigations. In the context of financial engineering, Chen, Li, Linton and Lu consider the dynamic portfolio choice problem with multiple conditioning variables. They estimate the optimal choice in a practically implementable nonparametric manner, i.e. to estimate the marginal optimal portfolio for each univariate conditioning variable, and then to construct the joint optimal solution by a weighted average of the marginal solutions. Conrad and Mammen have developed a complete asymptotic theory for qMLE of the GARCH-in-Mean model, which was missing in spite of the popularity of the model in practice. To examine financial extreme co-movements, Asimit, Gerrard, Hou and Peng investigate the properties of the limiting conditional Kendall’s tau and propose a nonparametric estimator for this measure. There are also three papers adapting time series or spatio-temporal models for specific applications. Duan proposes a novel and relatively simple model, the local-momentum AR model, for modeling interesting rate term structure. By forcing global mean-reverting but allowing local momentum preserving or building, this parsimonious model is able to capture observed salient features in interest rate time series. In Davis, Hancock and Yao, the theoretical properties of minimum description length is investigated when it is used for detecting the number and location of structure breaks in nonstationary time series. It has direct applications to identifying crisis and regime changes in economics and financial markets. A class of spatio-temporal models is studies by Dou, Parrella and Yao, which extends popular econometric spatial autoregressive panel data models by allowing the scalar coefficients for each location (or panel) to be different from each other. The extension is convincingly justified by the illustration with the consumer price index dynamics for the EU member states. To overcome the innate endogeneity, they propose a generalized Yule-Walker estimation method which applies the least squares estimation to a Yule-Walker equation. Finally we thank all the authors who contribute their new research results to this issue. We also thank the referees for their invaluable help in improving the quality of this final
2
product, and the liaising co-Editor, Jianqing Fan, for his indispensable guidance and help. We sincerely hope that this special issue will give you at least some part of the joy and the fun that we have had in editing it. Rong Chen1 Rutgers University, USA E-mail address: [email protected] Per Mykland University of Chicago, USA Qiwei Yao London School of Economics and Political Science, UK
1
Corresponding editor
3