RiskMetrics™ —Technical Document

60 Chapter 4. Statistical and probability foundations
Charts 4.10 and 4.11 show time series of squared returns for the USD/DEM exchange rate and for
the S&P 500 index.
Chart 4.10
USD/DEM returns squared
USD/DEM log returns squared (%)
18
16
14
12
10
8
6
4
2
0
1990 1991 1992 1993 1994 1995 1996
Chart 4.11
S&P 500 returns squared
S&P 500 log returns squared (%)
14
12
10
8
6
4
2
0
1990 1991 1992 1993 1994 1995 1996
Notice the clusters of large and small spikes in both series. These clusters represent periods of high
and low volatility recognized in Section 4.2.1. To analyze the autocorrelation structure of the
squared returns, as in the case of log price changes, we compute sample autocorrelation coefficients
and the Box-Ljung statistic. Charts 4.12 and 4.13 present correlograms for the squared
return series of USD/DEM foreign exchange and S&P 500, respectively.
RiskMetrics —Technical Document
Fourth Edition