RUEY S. TSAY, PhD, is H.G.B. Alexander Professor of Econometrics and Statistics at The University of Chicago Booth School of Business. Dr. Tsay has written over 100 published articles in the areas of business and economic forecasting, data analysis, risk management, and process control. A Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and Academia Sinica, Dr. Tsay is author of Analysis of Financial Time Series, Third Edition and coauthor of A Course in Time Series Analysis.

• Preface xiii1 FINANCIAL DATA AND THEIR PROPERTIES 11.1 Asset Returns 21.2 Bond Yields and Prices 71.3 Implied Volatility 101.4 R Packages and Demonstrations 121.4.1 Installation of R Packages 121.4.2 The Quantmod Package 121.4.3 Some Basic R Commands 161.5 Examples of Financial Data 171.6 Distributional Properties of Returns 201.6.1 Review of Statistical Distributions and Their Moments 201.7 Visualization of Financial Data 271.8 Some Statistical Distributions 321.8.1 Normal Distribution 321.8.2 Lognormal Distribution 321.8.3 Stable Distribution 331.8.4 Scale Mixture of Normal Distributions 331.8.5 Multivariate Returns 34Exercises 36References 372 LINEAR MODELS FOR FINANCIAL TIME SERIES 392.1 Stationarity 402.2 Correlation and Autocorrelation Function 432.3 White Noise and Linear Time Series 502.4 Simple Autoregressive Models 512.4.1 Properties of AR Models 522.4.2 Identifying AR Models in Practice 602.4.3 Goodness of Fit 672.4.4 Forecasting 672.5 Simple Moving Average Models 692.5.1 Properties of MA Models 722.5.2 Identifying MA Order 732.5.3 Estimation 742.5.4 Forecasting Using MA Models 752.6 Simple ARMA Models 782.6.1 Properties of ARMA(1,1) Models 792.6.2 General ARMA Models 802.6.3 Identifying ARMA Models 812.6.4 Forecasting Using an ARMA Model 842.6.5 Three Model Representations for an ARMA Model 842.7 Unit-Root Nonstationarity 862.7.1 Random Walk 862.7.2 Random Walk with Drift 882.7.3 Trend-Stationary Time Series 902.7.4 General Unit-Root Nonstationary Models 912.7.5 Unit-Root Test 912.8 Exponential Smoothing 962.9 Seasonal Models 982.9.1 Seasonal Differencing 992.9.2 Multiplicative Seasonal Models 1012.9.3 Seasonal Dummy Variable 1072.10 Regression Models with Time Series Errors 1102.11 Long-Memory Models 1172.12 Model Comparison and Averaging 1202.12.1 In-sample Comparison 1202.12.2 Out-of-sample Comparison 1212.12.3 Model Averaging 125Exercises 125References 1273 CASE STUDIES OF LINEAR TIME SERIES 1283.1 Weekly Regular Gasoline Price 1293.1.1 Pure Time Series Model 1303.1.2 Use of Crude Oil Prices 1333.1.3 Use of Lagged Crude Oil Prices 1343.1.4 Out-of-Sample Predictions 1353.2 Global Temperature Anomalies 1403.2.1 Unit-Root Stationarity 1413.2.2 Trend-Nonstationarity 1453.2.3 Model Comparison 1483.2.4 Long-Term Prediction 1503.2.5 Discussion 1533.3 US Monthly Unemployment Rates 1573.3.1 Univariate Time Series Models 1573.3.2 An Alternative Model 1613.3.3 Model Comparison 1653.3.4 Use of Initial Jobless Claims 1653.3.5 Comparison 173Exercises 174References 1754 ASSET VOLATILITY AND VOLATILITY MODELS 1764.1 Characteristics of Volatility 1774.2 Structure of a Model 1784.3 Model Building 1814.4 Testing for ARCH Effect 1824.5 The ARCH Model 1854.5.1 Properties of ARCH Models 1864.5.2 Advantages and Weaknesses of ARCH Models 1874.5.3 Building an ARCH Model 1884.5.4 Some Examples 1934.6 The GARCH Model 1994.6.1 An Illustrative Example 2014.6.2 Forecasting Evaluation 2104.6.3 A Two-Pass Estimation Method 2104.7 The Integrated GARCH Model 2114.8 The GARCH-M Model 2134.9 The Exponential Garch Model 2154.9.1 An Illustrative Example 2174.9.2 An Alternative Model Form 2184.9.3 Second Example 2184.9.4 Forecasting Using an EGARCH Model 2204.10 The Threshold Garch Model 2224.11 Asymmetric Power ARCH Models 2244.12 Nonsymmetric GARCH Model 2264.13 The Stochastic Volatility Model 2284.14 Long-Memory Stochastic Volatility Models 2304.15 Alternative Approaches 2324.15.1 Use of High Frequency Data 2324.15.2 Use of Daily Open, High, Low, and Close Prices 235Exercises 239References 2415 APPLICATIONS OF VOLATILITY MODELS 2435.1 Garch Volatility Term Structure 2445.1.1 Term Structure 2465.2 Option Pricing and Hedging 2485.3 Time-Varying Correlations and Betas 2515.3.1 Time-Varying Betas 2565.4 Minimum Variance Portfolios 2595.5 Prediction 263Exercises 271References 2726 HIGH FREQUENCY FINANCIAL DATA 2746.1 Nonsynchronous Trading 2756.2 Bid–Ask Spread of Trading Prices 2796.3 Empirical Characteristics of Trading Data 2826.4 Models for Price Changes 2856.4.1 Ordered Probit Model 2886.4.2 A Decomposition Model 2936.5 Duration Models 2986.5.1 Diurnal Component 2996.5.2 The ACD Model 3016.5.3 Estimation 3036.6 Realized Volatility 3086.6.1 Handling Microstructure Noises 3136.6.2 Discussion 317Appendix A: Some Probability Distributions 320Appendix B: Hazard Function 323Exercises 324References 3257 VALUE AT RISK 3277.1 Risk Measure and Coherence 3287.1.1 Value at Risk (VaR) 3297.1.2 Expected Shortfall 3347.2 Remarks on Calculating Risk Measures 3367.3 Riskmetrics 3377.3.1 Discussion 3427.3.2 Multiple Positions 3437.4 An Econometric Approach 3457.4.1 Multiple Periods 3487.5 Quantile Estimation 3527.5.1 Quantile and Order Statistics 3537.5.2 Quantile Regression 3547.6 Extreme Value Theory 3587.6.1 Review of Extreme Value Theory 3587.6.2 Empirical Estimation 3617.6.3 Application to Stock Returns 3637.7 An Extreme Value Approach to Var 3687.7.1 Discussion 3707.7.2 Multiperiod VaR 3717.7.3 Return Level 3717.8 Peaks Over Thresholds 3727.8.1 Statistical Theory 3737.8.2 Mean Excess Function 3747.8.3 Estimation 3767.8.4 An Alternative Parameterization 3787.9 The Stationary Loss Processes 381Exercises 383References 384Index 387

“I found this book highly informative and interesting to read. The proper mix of theory and hands-on programming examples makes it recommended reading for both R programmers interested in finance and financial analysts with a basic programming background. Well written and following a clear and defined logical layout, the author has written a current reference text on using a powerful open-source programming language for typical financial analysis.”  (Computing Reviews, 25 March 2014)“All in all, this book is a good and useful introduction to financial time series with many real-world examples. It is suitable for use both as a textbook and for self-study, with exercises provided at the end of each chapter.”  (International Statistical Review, 14 June 2013)

RUEY S. TSAY, PhD, is H.G.B. Alexander Professor of Econometrics and Statistics at The University of Chicago Booth School of Business. Dr. Tsay has written over 100 published articles in the areas of business and economic forecasting, data analysis, risk management, and process control. A Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and Academia Sinica, Dr. Tsay is author of Analysis of Financial Time Series, Third Edition and coauthor of A Course in Time Series Analysis.

• Preface xiii1 FINANCIAL DATA AND THEIR PROPERTIES 11.1 Asset Returns 21.2 Bond Yields and Prices 71.3 Implied Volatility 101.4 R Packages and Demonstrations 121.4.1 Installation of R Packages 121.4.2 The Quantmod Package 121.4.3 Some Basic R Commands 161.5 Examples of Financial Data 171.6 Distributional Properties of Returns 201.6.1 Review of Statistical Distributions and Their Moments 201.7 Visualization of Financial Data 271.8 Some Statistical Distributions 321.8.1 Normal Distribution 321.8.2 Lognormal Distribution 321.8.3 Stable Distribution 331.8.4 Scale Mixture of Normal Distributions 331.8.5 Multivariate Returns 34Exercises 36References 372 LINEAR MODELS FOR FINANCIAL TIME SERIES 392.1 Stationarity 402.2 Correlation and Autocorrelation Function 432.3 White Noise and Linear Time Series 502.4 Simple Autoregressive Models 512.4.1 Properties of AR Models 522.4.2 Identifying AR Models in Practice 602.4.3 Goodness of Fit 672.4.4 Forecasting 672.5 Simple Moving Average Models 692.5.1 Properties of MA Models 722.5.2 Identifying MA Order 732.5.3 Estimation 742.5.4 Forecasting Using MA Models 752.6 Simple ARMA Models 782.6.1 Properties of ARMA(1,1) Models 792.6.2 General ARMA Models 802.6.3 Identifying ARMA Models 812.6.4 Forecasting Using an ARMA Model 842.6.5 Three Model Representations for an ARMA Model 842.7 Unit-Root Nonstationarity 862.7.1 Random Walk 862.7.2 Random Walk with Drift 882.7.3 Trend-Stationary Time Series 902.7.4 General Unit-Root Nonstationary Models 912.7.5 Unit-Root Test 912.8 Exponential Smoothing 962.9 Seasonal Models 982.9.1 Seasonal Differencing 992.9.2 Multiplicative Seasonal Models 1012.9.3 Seasonal Dummy Variable 1072.10 Regression Models with Time Series Errors 1102.11 Long-Memory Models 1172.12 Model Comparison and Averaging 1202.12.1 In-sample Comparison 1202.12.2 Out-of-sample Comparison 1212.12.3 Model Averaging 125Exercises 125References 1273 CASE STUDIES OF LINEAR TIME SERIES 1283.1 Weekly Regular Gasoline Price 1293.1.1 Pure Time Series Model 1303.1.2 Use of Crude Oil Prices 1333.1.3 Use of Lagged Crude Oil Prices 1343.1.4 Out-of-Sample Predictions 1353.2 Global Temperature Anomalies 1403.2.1 Unit-Root Stationarity 1413.2.2 Trend-Nonstationarity 1453.2.3 Model Comparison 1483.2.4 Long-Term Prediction 1503.2.5 Discussion 1533.3 US Monthly Unemployment Rates 1573.3.1 Univariate Time Series Models 1573.3.2 An Alternative Model 1613.3.3 Model Comparison 1653.3.4 Use of Initial Jobless Claims 1653.3.5 Comparison 173Exercises 174References 1754 ASSET VOLATILITY AND VOLATILITY MODELS 1764.1 Characteristics of Volatility 1774.2 Structure of a Model 1784.3 Model Building 1814.4 Testing for ARCH Effect 1824.5 The ARCH Model 1854.5.1 Properties of ARCH Models 1864.5.2 Advantages and Weaknesses of ARCH Models 1874.5.3 Building an ARCH Model 1884.5.4 Some Examples 1934.6 The GARCH Model 1994.6.1 An Illustrative Example 2014.6.2 Forecasting Evaluation 2104.6.3 A Two-Pass Estimation Method 2104.7 The Integrated GARCH Model 2114.8 The GARCH-M Model 2134.9 The Exponential Garch Model 2154.9.1 An Illustrative Example 2174.9.2 An Alternative Model Form 2184.9.3 Second Example 2184.9.4 Forecasting Using an EGARCH Model 2204.10 The Threshold Garch Model 2224.11 Asymmetric Power ARCH Models 2244.12 Nonsymmetric GARCH Model 2264.13 The Stochastic Volatility Model 2284.14 Long-Memory Stochastic Volatility Models 2304.15 Alternative Approaches 2324.15.1 Use of High Frequency Data 2324.15.2 Use of Daily Open, High, Low, and Close Prices 235Exercises 239References 2415 APPLICATIONS OF VOLATILITY MODELS 2435.1 Garch Volatility Term Structure 2445.1.1 Term Structure 2465.2 Option Pricing and Hedging 2485.3 Time-Varying Correlations and Betas 2515.3.1 Time-Varying Betas 2565.4 Minimum Variance Portfolios 2595.5 Prediction 263Exercises 271References 2726 HIGH FREQUENCY FINANCIAL DATA 2746.1 Nonsynchronous Trading 2756.2 Bid–Ask Spread of Trading Prices 2796.3 Empirical Characteristics of Trading Data 2826.4 Models for Price Changes 2856.4.1 Ordered Probit Model 2886.4.2 A Decomposition Model 2936.5 Duration Models 2986.5.1 Diurnal Component 2996.5.2 The ACD Model 3016.5.3 Estimation 3036.6 Realized Volatility 3086.6.1 Handling Microstructure Noises 3136.6.2 Discussion 317Appendix A: Some Probability Distributions 320Appendix B: Hazard Function 323Exercises 324References 3257 VALUE AT RISK 3277.1 Risk Measure and Coherence 3287.1.1 Value at Risk (VaR) 3297.1.2 Expected Shortfall 3347.2 Remarks on Calculating Risk Measures 3367.3 Riskmetrics 3377.3.1 Discussion 3427.3.2 Multiple Positions 3437.4 An Econometric Approach 3457.4.1 Multiple Periods 3487.5 Quantile Estimation 3527.5.1 Quantile and Order Statistics 3537.5.2 Quantile Regression 3547.6 Extreme Value Theory 3587.6.1 Review of Extreme Value Theory 3587.6.2 Empirical Estimation 3617.6.3 Application to Stock Returns 3637.7 An Extreme Value Approach to Var 3687.7.1 Discussion 3707.7.2 Multiperiod VaR 3717.7.3 Return Level 3717.8 Peaks Over Thresholds 3727.8.1 Statistical Theory 3737.8.2 Mean Excess Function 3747.8.3 Estimation 3767.8.4 An Alternative Parameterization 3787.9 The Stationary Loss Processes 381Exercises 383References 384Index 387

“I found this book highly informative and interesting to read. The proper mix of theory and hands-on programming examples makes it recommended reading for both R programmers interested in finance and financial analysts with a basic programming background. Well written and following a clear and defined logical layout, the author has written a current reference text on using a powerful open-source programming language for typical financial analysis.”  (Computing Reviews, 25 March 2014)“All in all, this book is a good and useful introduction to financial time series with many real-world examples. It is suitable for use both as a textbook and for self-study, with exercises provided at the end of each chapter.”  (International Statistical Review, 14 June 2013)

RUEY S. TSAY, PhD, is H.G.B. Alexander Professor of Econometrics and Statistics at The University of Chicago Booth School of Business. Dr. Tsay has written over 100 published articles in the areas of business and economic forecasting, data analysis, risk management, and process control. A Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and Academia Sinica, Dr. Tsay is author of Analysis of Financial Time Series, Third Edition and coauthor of A Course in Time Series Analysis.

• Preface xiii1 FINANCIAL DATA AND THEIR PROPERTIES 11.1 Asset Returns 21.2 Bond Yields and Prices 71.3 Implied Volatility 101.4 R Packages and Demonstrations 121.4.1 Installation of R Packages 121.4.2 The Quantmod Package 121.4.3 Some Basic R Commands 161.5 Examples of Financial Data 171.6 Distributional Properties of Returns 201.6.1 Review of Statistical Distributions and Their Moments 201.7 Visualization of Financial Data 271.8 Some Statistical Distributions 321.8.1 Normal Distribution 321.8.2 Lognormal Distribution 321.8.3 Stable Distribution 331.8.4 Scale Mixture of Normal Distributions 331.8.5 Multivariate Returns 34Exercises 36References 372 LINEAR MODELS FOR FINANCIAL TIME SERIES 392.1 Stationarity 402.2 Correlation and Autocorrelation Function 432.3 White Noise and Linear Time Series 502.4 Simple Autoregressive Models 512.4.1 Properties of AR Models 522.4.2 Identifying AR Models in Practice 602.4.3 Goodness of Fit 672.4.4 Forecasting 672.5 Simple Moving Average Models 692.5.1 Properties of MA Models 722.5.2 Identifying MA Order 732.5.3 Estimation 742.5.4 Forecasting Using MA Models 752.6 Simple ARMA Models 782.6.1 Properties of ARMA(1,1) Models 792.6.2 General ARMA Models 802.6.3 Identifying ARMA Models 812.6.4 Forecasting Using an ARMA Model 842.6.5 Three Model Representations for an ARMA Model 842.7 Unit-Root Nonstationarity 862.7.1 Random Walk 862.7.2 Random Walk with Drift 882.7.3 Trend-Stationary Time Series 902.7.4 General Unit-Root Nonstationary Models 912.7.5 Unit-Root Test 912.8 Exponential Smoothing 962.9 Seasonal Models 982.9.1 Seasonal Differencing 992.9.2 Multiplicative Seasonal Models 1012.9.3 Seasonal Dummy Variable 1072.10 Regression Models with Time Series Errors 1102.11 Long-Memory Models 1172.12 Model Comparison and Averaging 1202.12.1 In-sample Comparison 1202.12.2 Out-of-sample Comparison 1212.12.3 Model Averaging 125Exercises 125References 1273 CASE STUDIES OF LINEAR TIME SERIES 1283.1 Weekly Regular Gasoline Price 1293.1.1 Pure Time Series Model 1303.1.2 Use of Crude Oil Prices 1333.1.3 Use of Lagged Crude Oil Prices 1343.1.4 Out-of-Sample Predictions 1353.2 Global Temperature Anomalies 1403.2.1 Unit-Root Stationarity 1413.2.2 Trend-Nonstationarity 1453.2.3 Model Comparison 1483.2.4 Long-Term Prediction 1503.2.5 Discussion 1533.3 US Monthly Unemployment Rates 1573.3.1 Univariate Time Series Models 1573.3.2 An Alternative Model 1613.3.3 Model Comparison 1653.3.4 Use of Initial Jobless Claims 1653.3.5 Comparison 173Exercises 174References 1754 ASSET VOLATILITY AND VOLATILITY MODELS 1764.1 Characteristics of Volatility 1774.2 Structure of a Model 1784.3 Model Building 1814.4 Testing for ARCH Effect 1824.5 The ARCH Model 1854.5.1 Properties of ARCH Models 1864.5.2 Advantages and Weaknesses of ARCH Models 1874.5.3 Building an ARCH Model 1884.5.4 Some Examples 1934.6 The GARCH Model 1994.6.1 An Illustrative Example 2014.6.2 Forecasting Evaluation 2104.6.3 A Two-Pass Estimation Method 2104.7 The Integrated GARCH Model 2114.8 The GARCH-M Model 2134.9 The Exponential Garch Model 2154.9.1 An Illustrative Example 2174.9.2 An Alternative Model Form 2184.9.3 Second Example 2184.9.4 Forecasting Using an EGARCH Model 2204.10 The Threshold Garch Model 2224.11 Asymmetric Power ARCH Models 2244.12 Nonsymmetric GARCH Model 2264.13 The Stochastic Volatility Model 2284.14 Long-Memory Stochastic Volatility Models 2304.15 Alternative Approaches 2324.15.1 Use of High Frequency Data 2324.15.2 Use of Daily Open, High, Low, and Close Prices 235Exercises 239References 2415 APPLICATIONS OF VOLATILITY MODELS 2435.1 Garch Volatility Term Structure 2445.1.1 Term Structure 2465.2 Option Pricing and Hedging 2485.3 Time-Varying Correlations and Betas 2515.3.1 Time-Varying Betas 2565.4 Minimum Variance Portfolios 2595.5 Prediction 263Exercises 271References 2726 HIGH FREQUENCY FINANCIAL DATA 2746.1 Nonsynchronous Trading 2756.2 Bid–Ask Spread of Trading Prices 2796.3 Empirical Characteristics of Trading Data 2826.4 Models for Price Changes 2856.4.1 Ordered Probit Model 2886.4.2 A Decomposition Model 2936.5 Duration Models 2986.5.1 Diurnal Component 2996.5.2 The ACD Model 3016.5.3 Estimation 3036.6 Realized Volatility 3086.6.1 Handling Microstructure Noises 3136.6.2 Discussion 317Appendix A: Some Probability Distributions 320Appendix B: Hazard Function 323Exercises 324References 3257 VALUE AT RISK 3277.1 Risk Measure and Coherence 3287.1.1 Value at Risk (VaR) 3297.1.2 Expected Shortfall 3347.2 Remarks on Calculating Risk Measures 3367.3 Riskmetrics 3377.3.1 Discussion 3427.3.2 Multiple Positions 3437.4 An Econometric Approach 3457.4.1 Multiple Periods 3487.5 Quantile Estimation 3527.5.1 Quantile and Order Statistics 3537.5.2 Quantile Regression 3547.6 Extreme Value Theory 3587.6.1 Review of Extreme Value Theory 3587.6.2 Empirical Estimation 3617.6.3 Application to Stock Returns 3637.7 An Extreme Value Approach to Var 3687.7.1 Discussion 3707.7.2 Multiperiod VaR 3717.7.3 Return Level 3717.8 Peaks Over Thresholds 3727.8.1 Statistical Theory 3737.8.2 Mean Excess Function 3747.8.3 Estimation 3767.8.4 An Alternative Parameterization 3787.9 The Stationary Loss Processes 381Exercises 383References 384Index 387

“I found this book highly informative and interesting to read. The proper mix of theory and hands-on programming examples makes it recommended reading for both R programmers interested in finance and financial analysts with a basic programming background. Well written and following a clear and defined logical layout, the author has written a current reference text on using a powerful open-source programming language for typical financial analysis.”  (Computing Reviews, 25 March 2014)“All in all, this book is a good and useful introduction to financial time series with many real-world examples. It is suitable for use both as a textbook and for self-study, with exercises provided at the end of each chapter.”  (International Statistical Review, 14 June 2013)