U.S. V- \ Ai\ Y'i   87 SO S2 95 97 00 UK. ^v^^Mk/J^A 0.1- 82 85 S7 90 92 95 97 00 Japan   0 5-------- .- 1 * 0.4-   /   03- 0.2 ■ ^ o.i-AvV r, H' J ! lb         62 85 87 SO S2 95 Germany S7 00       0.4-     ij 0.3-       \ it 0.2- 11   'V Jyi'l1 0-_ . . 82 85 87 90 92 95 97 FIGURE 1 G.1 Annualized Volatilities: Comparison between Constant and Time-Varying Estimates late significantly around the constant estimate. For example, the annualized constant volatility for the U.S. equity market is equal to 16.06 percent in our sample. However, over the same period, the time-varying estimate oscillates between a maximum of 48.49 percent and a minimum of 6.51 percent. The evidence is similar for the other three markets. The question is whether the fluctuations generated by the second estimator reflect actual variations in market volatility or are the consequence of noise in the data. In fact, one could argue that the rolling window is too short and, therefore, too sensitive to the addition/deletion of a single large observation. To address this issue, we perform a simple exercise based on a technique known as Monte Carlo simulation. A typical Monte Carlo simulation is performed as follows. Start by postulating a null hypothesis to be tested. In our case, we postulate that the annual volatility of the U.S. market between 1980 and 2002 is constant and equal to 16.06 percent. Second, generate a large number of histories (time series of data) assuming that the null hypothesis is true. For our exercise, we generated 1,000 histories, each containing 5,850 observations, assuming that the data were drawn from a normal distribution with an annual volatility of 16.06 percent. For each history, we constructed the time series of volatilities based on the rolling window technique, and computed the average absolute deviation (aad) between those volatilities and the postulated true volatility. Since we generated 1,000 histories, we were able to