Event-Based Measures of Financial Time

A bar is a sampling rule, not a neutral container. The notebooks compare several ways to measure financial time and show how imbalance and run bars stop when directional evidence crosses a stated threshold.

The central relation

A transaction record and its dollar value can be written as

(t_i,p_i,v_i)_{i=1}^{n},\qquad d_i=p_iv_i.

$i$ identifies a transaction, $t_i$ is its time, $p_i$ its price, and $v_i$ its volume. The product $d_i$ is dollar value. Different clocks accumulate records, volume, or dollar value before closing a bar.

How trading activity changes the financial clock

The figures compare ordinary clock time with activity-based clocks and then trace the stopping paths used by imbalance and run bars.

Clock, tick, volume, and dollar bars formed from the same transaction sequence. — The same records produce different bar locations under clock, tick, volume, and dollar time. Activity-based clocks place more bars where trading is concentrated.

Cumulative imbalance and directional-run paths with their stopping thresholds. — The paths show the evidence accumulated before each stopping rule closes a bar. The threshold and expected imbalance determine the resulting bar lengths.

Changing the clock changes the sample presented to every later method. It does not create information that was absent from the underlying record.

Notebooks


1. Choosing a financial clock
2. Imbalance Bars as Stopping Times
3. Sampling directional runs by information