Figure 6

The effect of the smoothing bandwidth on the travel time estimates. In Panel A we show the distribution of the lower bound estimates normalized by subtracting the lower bound estimate obtained with smoothing bandwidth of 30 minutes. In Panel B we show the distribution of similarly normalized peak estimates. In both panels the outer shaded area denotes the 5th and 95th percentile, the inner shaded area denotes the 25th and 95th percentiles of all estimates, and the solid lines correspond to the median of all the normalized estimates. In these plots, we only show data for OD pairs with at least 10,000 data points. Furthermore, the results for the lower bound estimates are only based on those results for which we are able to identify the lower bound with all different bandwidth values. (With some OD pairs the inter-observation time distribution never falls to half of the identified peak’s width on the peak’s left hand side due to data irregularities.) Panel B shows that most peak estimates tend to stabilize when the width of the smoothing kernel reaches 20 min, as is shown by the 5th percentile of the normalized estimates. Additionally, we note that smoothing causes a systematic bias to the results: the larger the kernel width, the larger are the peak estimates and the smaller are the lower bound estimates.