˲ They receive large amounts of data every microsecond.

˲ They must be able to act extremely fast on the received data, as the profitability of the signals they are observing decays very quickly.

Online algorithms provide a natural class of algorithms suitable for HFT applications. In an online problem, new input variables are revealed sequentially. After each new input the algorithm needs to make a decision—for example, whether or not to submit a trade.

This is in stark contrast to an offline
problem, which assumes the entire in-
put data is available at the time of the
decision making. Many practical opti-
mization problems addressed in com-
puter science and operations research
applications are online problems. 1
Besides solving an online problem,
HFT algorithms also need to react ex-
tremely fast to market updates. To
guarantee a fast reaction time, efficient
memory handling becomes a necessity
for a live trading algorithm. Keeping a
large amount of data in memory will
slow down any CPU, so it is important
that an algorithm uses only a minimal
amount of data and parameters, which
can be stored in fast accessible mem-
ory such as the L1 cache. In addition,
these factors should reflect the current
state of the market and must be updat-
ed in real time when new data points
are observed. In summary, the smaller
the number of factors that need to be
kept in memory and the simpler the
computation required to update each
factor, the faster an algorithm is able
to react to market updates.
Based on the speed requirement
and the online nature of HFT prob-
lems, the class of one-pass algorithms
is especially suitable for HFT applica-
tions. These algorithms receive one
data point at a time and use it to up-
date a set of factors. After the updat-
ing, the data point is discarded and
only the updated factors are kept in
memory.

In this article we discuss three estimation problems that can arise in HFT algorithms and that can be ef-