An Introduction to Analysis of Financial Data with R E-Book

Ruey S. Tsay

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch

Seitenzahl: 543

Veröffentlichungsjahr: 2014

Beschreibung

A complete set of statistical tools for beginning financial analysts from a leading authority

Written by one of the leading experts on the topic, An Introduction to Analysis of Financial Data with R explores basic concepts of visualization of financial data. Through a fundamental balance between theory and applications, the book supplies readers with an accessible approach to financial econometric models and their applications to real-world empirical research.

The author supplies a hands-on introduction to the analysis of financial data using the freely available R software package and case studies to illustrate actual implementations of the discussed methods. The book begins with the basics of financial data, discussing their summary statistics and related visualization methods. Subsequent chapters explore basic time series analysis and simple econometric models for business, finance, and economics as well as related topics including:

• Linear time series analysis, with coverage of exponential smoothing for forecasting and methods for model comparison
• Different approaches to calculating asset volatility and various volatility models
• High-frequency financial data and simple models for price changes, trading intensity, and realized volatility
• Quantitative methods for risk management, including value at risk and conditional value at risk
• Econometric and statistical methods for risk assessment based on extreme value theory and quantile regression

Throughout the book, the visual nature of the topic is showcased through graphical representations in R, and two detailed case studies demonstrate the relevance of statistics in finance. A related website features additional data sets and R scripts so readers can create their own simulations and test their comprehension of the presented techniques.

An Introduction to Analysis of Financial Data with R is an excellent book for introductory courses on time series and business statistics at the upper-undergraduate and graduate level. The book is also an excellent resource for researchers and practitioners in the fields of business, finance, and economics who would like to enhance their understanding of financial data and today's financial markets.

Leseprobe

Contents

1 FINANCIAL DATA AND THEIPROPERTIE

1.1 ASSET RETURNS

1.2 BOND YIELDS AND PRICES

1.3 IMPLIED VOLATILITY

1.4 R PACKAGES AND DEMONSTRATIONS

1.5 EXAMPLES OF FINANCIAL DATA

1.6 DISTRIBUTIONAL PROPERTIES OF RETURNS

1.7 VISUALIZATION OF FINANCIAL DATA

1.8 SOME STATISTICAL DISTRIBUTIONS

2 LINEAR MODELS FOR FINANCIAL TIME SERIES

2.1 STATIONARITY

2.2 CORRELATION AND AUTOCORRELATION FUNCTION

2.3 WHITE NOISE AND LINEAR TIME SERIES

2.4 SIMPLE AUTOREGRESSIVE MODELS

2.5 SIMPLE MOVING AVERAGE MODELS

2.6 SIMPLE ARMA MODELS

2.7 UNIT-ROOT NONSTATIONARITY

2.8 EXPONENTIAL SMOOTHING

2.9 SEASONAL MODELS

2.10 REGRESSION MODELS WITH TIME SERIES ERRORS

2.11 LONG-MEMORY MODELS

2.12 MODEL COMPARISON AND AVERAGING

3 CASE STUDIES OF LINEAR TIME SERIES

3.1 WEEKLY REGULAR GASOLINE PRICE

3.2 GLOBAL TEMPERATURE ANOMALIES

3.3 US MONTHLY UNEMPLOYMENT RATES

4 ASSET VOLATILITY AND VOLATILITY MODELS

4.1 CHARACTERISTICS OF VOLATILITY

4.2 STRUCTURE OF A MODEL

4.3 MODEL BUILDING

4.4 TESTING FOR ARCH EFFECT

4.5 THE ARCH MODEL

4.6 THE GARCH MODEL

4.7 THE INTEGRATED GARCH MODEL

4.8 THE GARCH-M MODEL

4.9 THE EXPONENTIAL GARCH MODEL

4.10 THE THRESHOLD GARCH MODEL

4.11 ASYMMETRIC POWER ARCH MODELS

4.12 NONSYMMETRIC GARCH MODEL

4.13 THE STOCHASTIC VOLATILITY MODEL

4.14 LONG-MEMORY STOCHASTIC VOLATILITY MODELS

4.15 ALTERNATIVE APPROACHES

5 APPLICATIONS OF VOLATILITY MODELS

5.1 GARCH VOLATILITY TERM STRUCTURE

5.2 OPTION PRICING AND HEDGING

5.3 TIME-VARYING CORRELATIONS AND BETAS

5.4 MINIMUM VARIANCE PORTFOLIOS

5.5 PREDICTION

6 HIGH FREQUENCY FINANCIAL DATA

6.1 NONSYNCHRONOUS TRADING

6.2 BID–ASK SPREAD OF TRADING PRICES

6.3 EMPIRICAL CHARACTERISTICS OF TRADING DATA

6.4 MODELS FOR PRICE CHANGES

6.5 DURATION MODELS

6.6 REALIZED VOLATILITY

7 VALUE AT RISK

7.1 RISK MEASURE AND COHERENCE

7.2 REMARKS ON CALCULATING RISK MEASURES

7.3 RISKMETRICS

7.4 AN ECONOMETRIC APPROACH

7.5 QUANTILE ESTIMATION

7.6 EXTREME VALUE THEORY

7.7 AN EXTREME VALUE APPROACH TO VAR

7.8 PEAKS OVER THRESHOLDS

7.9 THE STATIONARY LOSS PROCESSES

INDEX

WILEY SERIES IN PROBABILITY AND STATISTICS

Established by WALTER A. SHEWHART and SAMUEL S. WILKS

Editors: David J. Balding. Noel A. C. Cressie, Garrett M. Fitzmaurice, Harvey Goldstein, lain M. Johnstone, Geert Molenherghs, David w. Scott, Adrian F. M. Smith. Ruey S. Tsay, Sanford Weisberg

Editors Emeriti: Vic Barnett, J. Stuart Hunter, Joseph B. Kadane, JozefL. Teugels

cover image: Courtesy of Ruey S. Tsay

Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Tsay, Ruey S.,

An introduction to analysis of financial data with R/Ruey S. Tsay.

p. cm.

Includes index.

ISBN 978-0-470-89081-3 (cloth)

1. Finance–Econometric models. 2. Time-series analysis. 3. Econometrics. 4. R (Computer program language) I. Title.

HG106.T76 2012

332.0285′ 133–dc23

2012002912

To Teresa

PREFACE

I am often asked by readers of Analysis of Financial Time Series: Can you make the analysis of financial data easier? I am also asked by my students: How to simplify the empirical work and what is the relevance of statistics to finance? These are important questions. They motivate me to write this introductory text.

To simplify empirical data analysis, I decided to use R for all analyses. My decision is based on several reasons. First, R is free and available for most operating systems. Second, many researchers have developed nice packages for analyzing financial data, especially RMetrics has many useful packages. Third, the capability of R packages improves dramatically and rapidly. This trend is expected to continue. Fourth, I wrote some simple R scripts to perform specific analyses in several places. These scripts serve two purposes. They attain to the special need I have in presenting the concepts and methods. More importantly, they demonstrate that once a reader has some experience with R, he/she can easily tailor R commands and scripts into his/her need to simplify analysis of financial data.

To simplify the concept of econometric and statistical theory, I tried to present it in a concise manner and used extensively real examples in demonstration. The book has seven chapters; two of them are case studies. These two chapters demonstrate the relevance of statistics in finance. The other chapters are organized to help readers understand the concepts of and gain experience in analyzing financial data. Chapter 1 introduces financial data and discusses their summary statistics and visualization. It also introduces R so that readers can start to explore financial data. Chapter 2 provides basic knowledge of linear time series analysis. It covers simple econometric models that are useful in business, finance and economics. I tried to make the chapter as comprehensive as possible while keeping it concise. It includes exponential smoothing for forecasting and methods for model comparison. Chapter 3 considers three case studies. The models used are not simple, but they are designed to help readers understand the value and limitations of linear time series models in applications. Chapter 4 studies different approaches to calculate asset volatility and various volatility models. The approaches discussed include methods that use daily open, high, low and close stock prices. Again, I tried to make the chapter as comprehensive as possible while avoiding much of the heavy theory. Chapter 5 considers some applications of volatility models in finance. It is intended to help readers gain better insight into the term structure of volatility and use of volatility in financial applications. Chapter 6 deals with high-frequency financial data, including simple models for price changes and trading intensity and realized volatility. Finally, Chapter 7 studies quantitative methods for risk management, including value at risk and conditional value at risk. The chapter covers important econometric and statistical methods to assess risk, including those based on extreme value theory and quantile regression.

The book contains many plots and demonstrations. The goal is to simplify the analysis of financial data and to make the results easily understandable. Like many authors, I struggle to obtain a balance between the length of the book and new developments in financial econometrics. Omission of some important topics is unavoidable. There is some overlap with Analysis of Financial Time Series in coverage, but all examples are new.

I like to express my sincere thanks to my wife. Without her love and support, this book could not be written. I also like to thank my children; they are my inspiration and help me editing some chapters. Many readers and students constantly give me feedback and suggestions. Their input is invaluable. Finally, I like to thank Steve Quigley, Jacqueline Palmieri and their Wiley team for their support and encouragement.

The web page of the book is

http://faculty.chicagobooth.edu/ruey.tsay/teaching/introTS.

R. S. T.

Chicago, Illinois

October 2012

1

FINANCIAL DATA AND THEIR PROPERTIES

The importance of quantitative methods in business and finance has increased substantially in recent years because we are in a data-rich environment and the economies and financial markets are more integrated than ever before. Data are collected systematically for thousands of variables in many countries and at a finer timescale. Computing facilities and statistical packages for analyzing complicated and high dimensional financial data are now widely available. As a matter of fact, with an internet connection, one can easily download financial data from open sources within a software package such as R. All of these good features and capabilities are free and widely accessible.

The objective of this book is to provide basic knowledge of financial time series, introduce statistical tools useful for analyzing financial data, and gain experience in financial applications of various econometric methods. We begin with the basic concepts of financial data to be analyzed throughout the book. The software R is introduced via examples. We also discuss different ways to visualize financial data in R. Chapter 2 reviews basic concepts of linear time series analysis such as stationarity and autocorrelation function, introduces simple linear models for handling serial dependence of the data, and discusses regression models with time series errors, seasonality, unit-root nonstationarity, and long-memory processes. The chapter also considers exponential smoothing for forecasting and methods for model comparison. Chapter 3 considers some applications of the models introduced in Chapter 2 in the form of case studies. The goal is to help readers understand better data analysis, empirical modeling, and making inference. It also points out the limitations of linear time series models in long-term prediction. Chapter 4 focuses on modeling conditional heteroscedasticity (i.e., the conditional variance of an asset return). It introduces various econometric models for describing the evolution of asset volatility over time. The chapter also discusses alternative methods to volatility modeling, including use of daily high and low prices of an asset. In Chapter 5, we demonstrate some applications of volatility models using, again, some case studies. All steps for building volatility models are given, and the merits and weaknesses of various volatility models are discussed, including the connection to diffusion limit of continuous time models. Chapter 6 is concerned with analysis of high frequency financial data. It starts with special characteristics of high frequency data and gives models and methods that can be used to analyze such data. It shows that nonsynchronous trading and bid-ask bounce can introduce serial correlations in a stock return. It also studies the dynamic of time duration between trades and some econometric models for analyzing transaction data. In particular, we discuss the use of logistic linear regression and probit models to study the stock price movements in consecutive trades. Finally, the chapter studies the realized volatility using intraday log returns. Chapter 7 discusses risk measures of a financial position and their use in risk management. It introduces value at risk and conditional value at risk to quantify the risk of a financial position within a holding period. It also provides various methods for calculating risk measures for a financial position, including RiskMetrics, econometric modeling, extreme value theory, quantile regression, and peaks over thresholds.

The book places great emphasis on application and empirical data analysis. Every chapter contains real examples, and, in many occasions, empirical characteristics of financial time series are used to motivate the development of econometric models. In some cases, simple R scripts are given on the web page for specific analysis. Many real data sets are also used in the exercises of each chapter.

1.1 ASSET RETURNS

Most financial studies involve returns, instead of prices, of assets. Campbell et al. (1997) give two main reasons for using returns. First, for average investors, return of an asset is a complete and scale-free summary of the investment opportunity. Second, return series are easier to handle than price series because the former have more attractive statistical properties. There are, however, several definitions of an asset return.

Let Pt be the price of an asset at time index t. We discuss some definitions of returns that are used throughout the book. Assume for the moment that the asset pays no dividends.

One-Period Simple Return. Holding the asset for one period from date t − 1 to date t would result in a simple gross return

(1.1)

The corresponding one-period simple net return or simple return is

(1.2)

Multiperiod Simple Return. Holding the asset for k periods between dates t − k and t gives a k-period simple gross return

Thus, the k-period simple gross return is just the product of the k one-period simple gross returns involved. This is called a compound return. The k-period simple net return is

In practice, the actual time interval is important in discussing and comparing returns (e.g., monthly return or annual return). If the time interval is not given, then it is implicitly assumed to be one year. If the asset was held for years, then the annualized (average) return is defined as