Weighting Samples with Overlapping Information

Two labeled observations can share much of the same price history. Treating them as independent gives repeated information too much influence. The notebooks measure this overlap and compare weighting and sampling rules.

The central relation

For event interval $[s_i,e_i]$ , concurrency is

I_{ti}=\mathbf 1\{s_i\leq t\leq e_i\},\qquad c_t=\sum_{i=1}^{n}I_{ti}.

$I_{ti}$ equals one when event $i$ is active at time $t$ . The start and end times are $s_i$ and $e_i$ , $n$ is the number of events, and $c_t$ counts how many events use information from time $t$ .

Measuring repeated information across event labels

The concurrency plot shows where labels reuse the same return intervals. The sampling comparison shows how sequential selection changes the uniqueness of the chosen sample.

Event intervals and the number of concurrently active labels through time. — Concurrency rises when many event horizons cover the same dates. Those periods contribute repeated information to several labels.

Average uniqueness under ordinary and sequential bootstrap sampling. — Sequential sampling favors observations that add information not already represented in the current draw. The comparison reports the resulting uniqueness rather than assuming independence.

Weights and sequential sampling reduce the influence of duplicated intervals, but they do not remove every form of dependence in financial observations.

Notebooks


1. Measuring overlap through event concurrency
2. Weighting returns by average uniqueness
3. Managing overlap with weights and sequential sampling