A second stability test concerns th

A second stability test concerns the impact that changes in the trading record have on the VPIN estimate. Small discrepancies in the trading record, such as missing trades, produce two effects. First, missing trades could alter the volume imbalance. But since we use an amount of volume equivalent to an entire trading session, this impact is expected to be negligible (the typical trade is for a few contracts, compared with the daily average of more than two million contracts traded on E-mini S&P 500 futures in 2010). The second effect of missing trades comes in the form of a shift in the VPIN trajectory. This impact can be evaluated by shifting the starting point of VPIN trajectories and calculating the cross-sectional standard deviations over time.
To assess the influence of different starting times, we compute 1,000 alternative VPIN trajectories for the E-mini S&P 500 futures, each starting one time bar after the previous one. We then take those 1,000 VPIN trajectories and align them for each time bar. Because VPIN is computed at the completion of each bucket, and buckets are not completed simultaneously, to each time bar we assign the last computed VPIN. We can then estimate a cross-sectional standard deviation on the difference between the first trajectory and the following 999. This estimate is likely to be greater than the true value of the standard deviation as a result of the asynchronicity in the completion of buckets.
Figure 5 shows that the cross-sectional standard deviation of differences on the 1,000 VPIN trajectories is negligible. That time series has a mean of 0.015, while VPIN’s average value is much greater (around 0.23). But as we argued earlier, the fact that buckets for each of the 1,000 trajectories are not completed simultaneously means that the true cross-sectional standard deviation is even smaller than this 0.015 average value. The spikes in cross-sectional standard deviations that are apparent in Figure 5 coincide with spikes in VPIN values. For example, on May 6, 2010, the cross-sectional standard deviation was just above 0.02, on a day when VPIN reached a level close to 0.5.
In conclusion, differences in the trading record due to missing transactions or alternative starting points do not seem to significantly impact VPIN estimates. To see this final point, consider two estimates of VPIN, one of 0.45, the other 0.5. This difference is well beyond what we see in Figure 5. Although the difference between these two VPIN estimates may seem large, they are not significantly different as the two VPIN estimates are at approximately the same point on the CDF of VPIN (0.991 compared with 0.995).

結果 (中文) 1:

第二次的稳定性测试关注交易记录的变化的影响对 VPIN 估计。细小的差异，在交易记录中，如缺少行业，有两个效果。第一，缺少行业可能会改变音量不平衡。但由于我们使用数量的体积相当于整个交易时段，预期这种影响可以忽略不计 （典型的贸易是为几个合同，相比平均每天超过 200 万的合约交易上电子迷你标准普尔指数期货在 2010 年）。缺少行业的第二个影响 VPIN 轨迹转变的形式出现。这种影响可以进行转移的起始点的 VPIN 轨迹和随着时间的推移计算截面的标准偏差。为了评估不同起始时代的香港，我们计算 1,000 替代 VPIN 轨迹，电子迷你标准普尔股指期货，每一前一后开始一个时间栏。采取这些 1,000 VPIN 轨迹，然后将它们对齐每个时间吧。因为 VPIN 被计算在每个存储桶，完成和水桶不同时，完成到我们分配每个时间栏最后计算 VPIN。然后，我们可以估计横断面的标准偏差，在第一批轨迹和以下 999 之间的区别。这估计是，可能要大于标准偏差由于异步完成的桶的真正价值。图 5 显示的差异对 1,000 VPIN 轨迹的横断面的标准偏差是可以忽略不计。那时间序列有平均值为 0.015，而 VPIN 的平均价值要大得多 （约 0.23)。但正如我们前文所述，水桶每个 1,000 轨迹不同时完成的事实意味着真实的横断面标准偏差甚至小于此 0.015 的平均价值。穗状花序在横断面是明显在图 5 中的标准偏差配合 VPIN 值中的峰值。例如，在 2010 年 5 月 6 日，横断面的标准偏差为上方 0.02，在 VPIN 达到接近 0.5 的水平时的一天。总之，由于缺少交易或替代起始点的交易记录中的差异似乎有力地影响 VPIN 估计做不。若要查看此单项点，请考虑两个估计的 VPIN，0.45，其他 0.5 之一。这种差异是远远超出我们在图 5 中看到了什么。尽管这两种的 VPIN 估计之间的区别可能看起来大，他们不是有力地不同，好象两个 VPIN 估计大约相同的点上 VPIN CDF (0.991 相比 0.995) 那样。