Trades arrive irregularly, with gaps from milliseconds to hours. Explain why a standard recurrent or convolutional model handles this badly, and give two modelling choices that account for the elapsed time correctly. State what each assumes.

Trades arrive irregularly, with gaps from milliseconds to hours. Explain why a standard recurrent or convolutional model handles this badly, and give two modelling choices that account for the elapsed time correctly. State what each assumes.

Approach: Ask what the model's notion of one step is and what it implicitly assumes about the interval between consecutive observations.

A standard recurrent or convolutional model treats one step as one fixed unit of time, so it applies the same state update whether the gap was one millisecond or one hour, and the fixes are either to make the state decay as a function of the elapsed time, as in a continuous-time state update, or to resample the series onto an event-based clock such as volume or trade-count bars. The implicit assumption in the standard model is uniform spacing, which is false for trades by construction and gives the model no way to distinguish a burst of activity from a quiet period, while both regimes carry very different information content per event. The first fix multiplies the hidden state by exp(-delta_t/tau) before each update, or solves a differential equation for the state between observations, which assumes the memory decays smoothly at a learned rate and that the gap itself is not informative beyond that decay. The second fix, sampling in volume or trade time, assumes the information arrival rate is proportional to the sampled quantity, which is close to true for volume and is why volume bars produce returns nearer to normally distributed with more stable variance. The gap should also be used as a feature in its own right, since the time between trades is itself predictive of volatility.

Follow-up: How would you build a model whose intensity of events and whose mark distribution are learned jointly, and what does the likelihood look like?

Key concepts: irregular sampling, elapsed time, exponential decay, state update.