As mentioned in a previous post, I intend to model quadratic variation in terms of multiple pairings of intensity (duration) and return level processes. At a minimum want a pairing for “non-jump” related returns and a pairing for “jump” related returns.
To do this it is necessary to partition returns into the categories based on threshold. We may further want to disregard price movements below a certain level unless they cumulatively add up to a return with significance within a period. Towards this end my duration measurement function uses a threshold to determine whether a return is to be considered as an event or not. In pseudocode:
r ← {0} ∪ diff(log(series))
t ← times (series)
durations ← {}
for (i in 2:length(r))
{
# determine cumulative return since last acceptance
cumr ← <cummulative return since last event or max cum window>
# determine whether qualifying event has occurred
if (|cumr| ≥ threshold or |r[i]| ≥ threshold)
durations ← durations ∪ {t[i] - <Tlastevent>}
}
For the diffusion portion of the process, in this 2 second sampled data set (EUR/USD low-liquidity period), a threshold of 3e-5 (equivalent of about 1/2 pip), seems to work well:
The jump portion of the process should be set so as to capture desired jump features and not much more, here I show with a threshold of 2e-4 (equivalent to about 3 pips):
Tr8dr 