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Introduction to Duration Models

In standard time series, time is fixed (every day). In HFT, time is random. The study of "How much time passes between two trades?" is modeled using Duration Models.

What is Duration (xi)?

Duration is the time interval between two consecutive events (trades).

  • xi = ti - t(i-1)

Interpreting Duration

  • Short Duration (Fast Trading): Indicates High Activity. Usually means informed traders are acting on news. "News Arrival".
  • Long Duration (Slow Trading): Indicates Low Activity. No news, or lack of liquidity.

The ACD Model

Robert Engle (Nobel winner) and Russell developed the Autoregressive Conditional Duration (ACD) model in 1998.

  • Concept: Just like GARCH models volatility clustering, ACD models Duration Clustering.
  • Clustering: Fast trading tends to follow fast trading. Slow periods tends to follow slow periods.

Formula Concept: Expected Duration today depends on:

  1. Average Duration (Baseline).
  2. Duration of the previous trade (Momentum).

Applications

  1. Liquidity Measurement: Short durations = High Liquidity.
  2. Probability of Informed Trading (PIN): If duration suddenly drops (trading speeds up), it's a signal that "Something is happening". Market Makers widen spreads immediately.
Note

Inverse Relationship: There is often an inverse relationship between Duration and Volatility.

  • Short Duration (Fast Trading) -> High Volatility.
  • Long Duration (Slow Trading) -> Low Volatility.

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