In a prior post mentioned that for intra-day variance prediction it made sense to separate variance into 2 processes:

**intensity process**

When is the next event going to occur; lets call this Tprior + Δt. This is the more complex process of the two to predict.
**power process**

What is the amplitude of the event at time Tnow + Δt. The power or amplitude process seems to be fairly well behaved. An ARMA style process seems like a likely candidate.

Towards this end, I have been exploring models for the intensity process. Very often this is modeled in terms of duration. Below is a summary of some results:

**ACD Models**

ACD processes make overreaching assumptions. In particular ACD models assume a constant AR decay and innovation contribution across time. Unfortunately this is not supported by empirical observations. Here are some results for the best-fitting Wiebull ACD model on HF data:

The R^2 level of 0.0091 does not inspire confidence.

**SVR Model**

I used an iterative non-parametric machine learning approach (SVR) with a training set of 20 prior observations and a lagged series of the derivatives of the prior 20 durations as the input vector. Training across the entire series, one gets an in-sample prediction R^2 of 0.9980. Unfortunately, incremental out of sample does not fair as well:

**Distribution of Durations**

Here are 2 views on the distribution of durations:

**Alternative Models**

Some possibilities:

**markov chain** (probabalistic state system)

We model the patterns by categorizing the durations into K separate levels. To train we observe the chain of states, say {K1, K8, K1,K1,K1,K4} and determine a graph describing the approximate event chains, factorizing and assigning probabilities.
**ANN**

Use a simple feed-forward network, trained with a GA or DE. This is easy to implement but subject to a variety of problems such as overfitting.

As the ANN is easy to compose, will start there.

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*Related*

Where did you end up on creating a model for predicting indtraday volatility?