Testing Jumps Via False Discovery Rate Control

Testing Jumps Via False Discovery Rate Control
Author: Yu-Min Yen
Publisher:
Total Pages: 42
Release: 2019
Genre:
ISBN:

Many recently developed nonparametric jump tests can be viewed as multiple hypothesis testing problems. For such multiple hypothesis tests, it is well known that controlling type I error often makes a large proportion of erroneous rejections, and such situation becomes even worse when the jump occurrence is a rare event. To obtain more reliable results, we aim to control the false discovery rate (FDR), an e fficient compound error measure for erroneous rejections in multiple testing problems. We perform the test via the Barndor -Nielsen and Shephard (BNS) test statistic, and control the FDR with the Benjamini and Hochberg (BH) procedure. We provide asymptotic results for the FDR control. From simulations, we examine relevant theoretical results and demonstrate the advantages of controlling the FDR. The hybrid approach is then applied to empirical analysis on two benchmark stock indices with high frequency data.

Testing and Detecting Jumps Based on a Discretely Observed Process

Testing and Detecting Jumps Based on a Discretely Observed Process
Author: Yingying Fan
Publisher:
Total Pages: 39
Release: 2009
Genre:
ISBN:

We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test statistic in A quot;{i}t-Sahalia and Jacod (2007), our new test statistic enjoys the same asymptotic properties but has smaller variance. These results are justified both theoretically and numerically. Thanks to the reduction of the variance, we also propose a new test procedure to identify the locations of jumps. The problem of jump identification thus reduces to a multiple comparison problem. We employ the False Discovery Rate (FDR) approach to control the type I error. Simulation studies and real data analysis further demonstrate the power of the newly proposed test method.

Multiple Testing and False Discovery Rate Control

Multiple Testing and False Discovery Rate Control
Author: Shiyun Chen
Publisher:
Total Pages: 142
Release: 2019
Genre:
ISBN:

Multiple testing, a situation where multiple hypothesis tests are performed simultaneously, is a core research topic in statistics that arises in almost every scientific field. When more hypotheses are tested, more errors are bound to occur. Controlling the false discovery rate (FDR) [BH95], which is the expected proportion of falsely rejected null hypotheses among all rejections, is an important challenge for making meaningful inferences. Throughout the dissertation, we analyze the asymptotic performance of several FDR-controlling procedures under different multiple testing settings. In Chapter 1, we study the famous Benjamini-Hochberg (BH) method [BH95] which often serves as benchmark among FDR-controlling procedures, and show that it is asymptotic optimal in a stylized setting. We then prove that a distribution-free FDR control method of Barber and Candès [FBC15], which only requires the (unknown) null distribution to be symmetric, can achieve the same asymptotic performance as the BH method, thus is also optimal. Chapter 2 proposes an interval-type procedure which identifies the longest interval with the estimated FDR under a given level and rejects the corresponding hypotheses with P-values lying inside the interval. Unlike the threshold approaches, this procedure scans over all intervals with the left point not necessary being zero. We show that this scan procedure provides strong control of the asymptotic false discovery rate. In addition, we investigate its asymptotic false non-discovery rate (FNR), deriving conditions under which it outperforms the BH procedure. In Chapter 3, we consider an online multiple testing problem where the hypotheses arrive sequentially in a stream, and investigate two procedures proposed by Javanmard and Montanari [JM15] which control FDR in an online manner. We quantify their asymptotic performance in the same location models as in Chapter 1 and compare their power with the (static) BH method. In Chapter 4, we propose a new class of powerful online testing procedures which incorporates the available contextual information, and prove that any rule in this class controls the online FDR under some standard assumptions. We also derive a practical algorithm that can make more empirical discoveries in an online fashion, compared to the state-of-the-art procedures.

Controlling the False Discovery Rate with Dynamic Adaptive Procedures and of Grouped Hypotheses

Controlling the False Discovery Rate with Dynamic Adaptive Procedures and of Grouped Hypotheses
Author: Peter W. MacDonald
Publisher:
Total Pages: 85
Release: 2018
Genre: Martingales (Mathematics)
ISBN:

In the multiple testing problem with independent tests, the classical Benjamini-Hochberg (BH) procedure controls the false discovery rate (FDR) below the target FDR level. Adaptive procedures can improve power by incorporating estimates of the proportion of true null hypotheses, which typically rely on a tuning parameter. Fixed adaptive procedures set their tuning parameters before seeing the data and can be shown to control the FDR in finite samples. In Chapter 2 of this thesis, we develop theoretical results for dynamic adaptive procedures whose tuning parameters are determined by the data. We show that, if the tuning parameter is chosen according to a left-to-right stopping time rule, the corresponding dynamic adaptive procedure controls the FDR in finite samples. Examples include the recently proposed right-boundary procedure and the widely used lowest-slope procedure, among others. Simulation results show that the right-boundary procedure is more powerful than other dynamic adaptive procedures under independence and mild dependence conditions. The BH procedure implicitly assumes all hypotheses are exchangeable. When hypotheses come from known groups, this assumption is inefficient, and power can be improved through a ranking of significance that incorporates group information. In Chapter 3 of this thesis, we define a general sequential framework for multiple testing procedures in the grouped setting. We develop a flexible grouped mirrored knockoff (GMK) procedure which approximates the optimal ranking of significance. We show that the GMK procedure controls the FDR in finite samples, and give a particular data-driven implementation using the expectation-maximization algorithm. Simulation and a real data example demonstrate that the GMK procedure outperforms its competitors in terms of power and FDR control with independent tests.

Financial Econometrics and Empirical Market Microstructure

Financial Econometrics and Empirical Market Microstructure
Author: Anil K. Bera
Publisher: Springer
Total Pages: 282
Release: 2014-11-18
Genre: Business & Economics
ISBN: 3319099469

In the era of Big Data our society is given the unique opportunity to understand the inner dynamics and behavior of complex socio-economic systems. Advances in the availability of very large databases, in capabilities for massive data mining, as well as progress in complex systems theory, multi-agent simulation and computational social science open the possibility of modeling phenomena never before successfully achieved. This contributed volume from the Perm Winter School address the problems of the mechanisms and statistics of the socio-economics system evolution with a focus on financial markets powered by the high-frequency data analysis. ​

Statistical Methods in the Atmospheric Sciences

Statistical Methods in the Atmospheric Sciences
Author: Daniel S. Wilks
Publisher: Academic Press
Total Pages: 697
Release: 2011-07-04
Genre: Science
ISBN: 0123850231

Statistical Methods in the Atmospheric Sciences, Third Edition, explains the latest statistical methods used to describe, analyze, test, and forecast atmospheric data. This revised and expanded text is intended to help students understand and communicate what their data sets have to say, or to make sense of the scientific literature in meteorology, climatology, and related disciplines. In this new edition, what was a single chapter on multivariate statistics has been expanded to a full six chapters on this important topic. Other chapters have also been revised and cover exploratory data analysis, probability distributions, hypothesis testing, statistical weather forecasting, forecast verification, and time series analysis. There is now an expanded treatment of resampling tests and key analysis techniques, an updated discussion on ensemble forecasting, and a detailed chapter on forecast verification. In addition, the book includes new sections on maximum likelihood and on statistical simulation and contains current references to original research. Students will benefit from pedagogical features including worked examples, end-of-chapter exercises with separate solutions, and numerous illustrations and equations. This book will be of interest to researchers and students in the atmospheric sciences, including meteorology, climatology, and other geophysical disciplines. Accessible presentation and explanation of techniques for atmospheric data summarization, analysis, testing and forecasting Many worked examples End-of-chapter exercises, with answers provided

Handbook of High-Frequency Trading and Modeling in Finance

Handbook of High-Frequency Trading and Modeling in Finance
Author: Ionut Florescu
Publisher: John Wiley & Sons
Total Pages: 414
Release: 2016-04-05
Genre: Business & Economics
ISBN: 1118593324

Reflecting the fast pace and ever-evolving nature of the financial industry, the Handbook of High-Frequency Trading and Modeling in Finance details how high-frequency analysis presents new systematic approaches to implementing quantitative activities with high-frequency financial data. Introducing new and established mathematical foundations necessary to analyze realistic market models and scenarios, the handbook begins with a presentation of the dynamics and complexity of futures and derivatives markets as well as a portfolio optimization problem using quantum computers. Subsequently, the handbook addresses estimating complex model parameters using high-frequency data. Finally, the handbook focuses on the links between models used in financial markets and models used in other research areas such as geophysics, fossil records, and earthquake studies. The Handbook of High-Frequency Trading and Modeling in Finance also features: • Contributions by well-known experts within the academic, industrial, and regulatory fields • A well-structured outline on the various data analysis methodologies used to identify new trading opportunities • Newly emerging quantitative tools that address growing concerns relating to high-frequency data such as stochastic volatility and volatility tracking; stochastic jump processes for limit-order books and broader market indicators; and options markets • Practical applications using real-world data to help readers better understand the presented material The Handbook of High-Frequency Trading and Modeling in Finance is an excellent reference for professionals in the fields of business, applied statistics, econometrics, and financial engineering. The handbook is also a good supplement for graduate and MBA-level courses on quantitative finance, volatility, and financial econometrics. Ionut Florescu, PhD, is Research Associate Professor in Financial Engineering and Director of the Hanlon Financial Systems Laboratory at Stevens Institute of Technology. His research interests include stochastic volatility, stochastic partial differential equations, Monte Carlo Methods, and numerical methods for stochastic processes. Dr. Florescu is the author of Probability and Stochastic Processes, the coauthor of Handbook of Probability, and the coeditor of Handbook of Modeling High-Frequency Data in Finance, all published by Wiley. Maria C. Mariani, PhD, is Shigeko K. Chan Distinguished Professor in Mathematical Sciences and Chair of the Department of Mathematical Sciences at The University of Texas at El Paso. Her research interests include mathematical finance, applied mathematics, geophysics, nonlinear and stochastic partial differential equations and numerical methods. Dr. Mariani is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley. H. Eugene Stanley, PhD, is William Fairfield Warren Distinguished Professor at Boston University. Stanley is one of the key founders of the new interdisciplinary field of econophysics, and has an ISI Hirsch index H=128 based on more than 1200 papers. In 2004 he was elected to the National Academy of Sciences. Frederi G. Viens, PhD, is Professor of Statistics and Mathematics and Director of the Computational Finance Program at Purdue University. He holds more than two dozen local, regional, and national awards and he travels extensively on a world-wide basis to deliver lectures on his research interests, which range from quantitative finance to climate science and agricultural economics. A Fellow of the Institute of Mathematics Statistics, Dr. Viens is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley.