1 CHAPTER 14 FORECASTING VOLATILITY II Figure 14.1 Autocorrelograms of the Squared Returns González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc.

2 Table 14.1 Descriptive Statistics of ARCH(1) Process and Standardized Process González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc ARCH(1)

3 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Figure 14.2 Simulated ARCH(1) Processes

4 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Figure 14.3 Autocorrelation Functions of ARCH(1) Process

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 5 Figure 14.4 Daily SP500 Returns and Autocorrelations of Squared Returns ARCH(p)

6 Figure 14.5 Low and High Persistence GARCH(1,1) Processes González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc GARCH(1,1)

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 7 Table 14.2 Descriptive Statistics of Low and High Persistence GARCH(1,1) Processes

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 8 Figure 14.6 Autocorrelation Functions of Low and High Persistence GARCH(1,1) Processes

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 9 Table 14.3 SP500 Daily Returns: Estimation of a GARCH(1,1) Model

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 10 Figure 14.7 Autocorrelation Function of the Standardized Squared Residuals from GARCH(1,1) for SP500 Daily Returns

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 11 Table 14.4 Maximum Likelihood Estimation of ARCH and GARCH Processes

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 12 Table 14.4 Maximum Likelihood Estimation of ARCH and GARCH Processes (continued)

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 13 Figure 14.8 Partition of One Trading Day in Time Intervals of Length 14.2 Realized Volatility

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 14 Table 14.5 Construction of Realized Volatility Measure …………………………………….

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 15 Figure 14.9 Daily Realized Variance of the SP500 Index Returns and its Autocorrelation Functions

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 16 Table 14.6 Model Estimation for Realized Variance and Autocorrelations of the Residuals of the Model

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 17 Table 14.6 Model Estimation for Realized Variance and Autocorrelations of the Residuals of the Model (continued)

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 18 Figure Descriptive Statistics of Realized and Log-Realized Variances

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 19 Figure Six Specifications for the Daily SP500 Index Conditional Variances

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 20 Table 14.7 Correlation Among Six Different Models of the Daily SP500 Conditional Variances