### Table 1: Comparison of Monte Carlo and quasi-Monte Carlo methods used to value a coupon bond

1998

"... In PAGE 21: ... For random Monte Carlo, the constant c is the standard deviation, and = :5. Table1 summarizes the results. For each method, the estimated size of the error at N = 10000 (based on the linear t), the convergence rate , and the approximate computation time for one run with this N are given.... In PAGE 25: ... Figure 2 displays these results in terms of the estimated computation time. In Table1 it can be seen that there is in fact a computational advantage to using quasi-random sequences over random for this problem. This is due to the time required for sequence generation.... ..."

Cited by 15

### Table 5 Lognormal investigation

"... In PAGE 15: ...2. Monte Carlo simulation: non-normal mixture target density Table5 presents results from Monte Carlo simulations comparing the perfor- mance of AKM and R amp;W on the standard lognormal target density (E[log X ]= 0; Var[log X ] = 1) at sample sizes n = 100 and n = 1000. The results are based on 100 Monte Carlo replicates.... ..."

### Table 4 Monte Carlo Evidence

2005

"... In PAGE 14: ... The results of the six experiments are presented in Table 4. Table 4 Panel A of Table4 gives the actual quarterly IMRF where the underlying model is difference stationary and three FRFs derived from three alternative estimation strategies. For all three estimation strategies the resulting FRFs give large values of persistence that grow with the time horizon.... In PAGE 15: ... What do we make of these results? First, we may ask what these results imply about the estimation strategy employed by forecasters. From Table4 we see that the strategy of estimating low order ARMA models, omitting a time trend and leaving the largest root unconstrained yield very large and increasing FRFs. Because these estimates are much higher than any observed from the actual forecast revisions in Table 3, we may conclude that forecasters have not used this strategy.... In PAGE 15: ... Because these estimates are much higher than any observed from the actual forecast revisions in Table 3, we may conclude that forecasters have not used this strategy. Table4 indicates that the strategy of imposing a time trend yields moderate estimates of persistence when the underlying process is a unit root but very low estimates when the true process is trend stationary. The latter case is inconsistent with observed FRFs from Table 3.... In PAGE 15: ... Finally, the strategy of imposing a unit root on low order AR models yields FRFs somewhat higher than those actually observed in Table 3. More generally, the results in Table4 suggest that annual FRFs will tend to be substantially larger than underlying quarterly IMRFs. In that sense, annual FRFs provide very poor and upwardly biased estimates of the underlying quarterly IMRF.... In PAGE 15: ... If our interest is obtaining the underlying IMRF from quarterly data, we may conclude that the large estimates of persistence found in the previous section are merely artifacts of the estimation process and have little bearing on the question of whether shocks to output are persistent. An alternative interpretation of the results in Table4 is warranted. The FRFs represent how forecasters actually revise their forecasts in light of new information and ... In PAGE 16: ... In practice, forecasters, and presumably economic agents, do not have precise knowledge of the underlying model and will use new information to update their model specification. In that sense, the results of Table4 can be interpreted as implying that IMRFs provide a poor estimate of how shocks affect our forecasts of future levels of output and hence are poor measures of the persistence of shocks. ... ..."

### Table 5: Estimated convergence rates.

2000

"... In PAGE 15: ... The estimated slopes of the linear ts obtained using ordinary least-squares. A selection of them are presented in Table5 . The estimated convergence rates for standard Monte Carlo vary from 0.... In PAGE 15: ...or standard Monte Carlo vary from 0.47 to 0.54. However, the theoretical convergence rate for Monte Carlo based on pseudo-random numbers is 0.5, so the estimates in Table5 are rather imprecise.... ..."

Cited by 7

### Table 1: Monte Carlo Experiments

"... In PAGE 9: ...or T = 20; 40; 60, we take both the univariate case and the bivariate case, i.e. k = 1; 2. The results are in Table1 , where AVE, SER, 10%, 25%, 50%, 75% and 90% denote the arithmetic average, the standard error, 10th, 25th, 50th, 75th and 90th percentiles from the 1000 estimates. For (a), the true parameter values are taken as 2 = 1 and R = 1.... ..."

### Table 8: Estimation of the variation of the Monte Carlo method.

2004

"... In PAGE 8: ... ^ (t) is used at the end for estimating P(Rn lt; t) and V ar(^ (t)) can be es- timated by ^ V ar(^ (t)) = ^ 2(t) B . Table8 gives the ^ (t) and a2 ^ V ar(^ (t)) based on n1 = 2000 and B = 200 samples. 8.... ..."

Cited by 4

### Table 7 Monte Carlo Analysis of Return Predictability

2003

"... In PAGE 21: ... For each replication, we estimate the unconstrained cross-sectionally restricted trivariate VAR(1) for returns, liquidity, and dividend yields using the pooled MLE methodology presented above. Table7 presents some relevant percentiles of the empirical distribution for the coefficients comprising the first row of A, and for their corresponding t-statistics. First we focus on the relation between returns and the lagged liquidity variable.... In PAGE 21: ... In sum, the Monte Carlo evidence shows that the impact of market liquidity on future returns is not a statistical artifact. Table7 also presents some relevant percentiles for the coefficient describing the relation- ship between returns and the lagged dividend yields. The median coefficient is 1.... ..."

Cited by 5

### Table 1. Monte Carlo simulated bias and standard deviation for a194 a16

in The Normal Inverse Gaussian Distribution: A Versatile Model For Heavy-Tailed Stochastic Processes

"... In PAGE 4: ....6. Performance evaluation We carried out a Monte Carlo simulation to assess the accuracy of the proposed estimator. The simulations are based on 1000 repeti- tions, and in Table1 we show the Monte Carlo bias and standard deviation of the estimator of the scale parameter a16 . The results are shown for various lengths a211 of the available data segments, and for two different values of a16 .... In PAGE 4: ... A relatively short range of a80 -values was used for obtaining the estimate of the characteristic function: a42 a125 a133 a55a39a80a43a55 a156 a125 a133 , and the kernel function was chosen to be a stan- dardized Gaussian. From Table1 we see that as expected, the accuracy becomes better as a211 increases. Both the bias and the standard deviation converges to zero as the sample size increases, so the proposed estimator is consistent.... ..."

### Table 1: Estimation of U Using Crude Monte Carlo and Balanced Failure Biasing

"... In PAGE 5: ... Assume that the network is functional if nodes 1 and 10 communicate (via a path with an operating component on each link). Table1 compares 90% confidence intervals for the limiting network unavailability from the crude Monte Carlo and BFB methods in regenerative simulations. The crude Monte Carlo simulation utilized 10,000,000 cycles to establish a benchmark.... ..."