Databases Reference
In-Depth Information
Additive Estimates
We need each of our estimates to be additive (which is why
we have a running variance estimate rather than a running
standard deviation estimate). If what we're after is a weighted
average, say, then we will need to have a running estimate of
both numerator and denominator.
If we want to be really careful about smoothness at the beginning
(which is more important if we have a few hundred data points or
fewer), then we'll actually vary the parameter
s
, via its reciprocal, which
we can think of as a kind of half-life. We start with a half-life of 1 and
grow it up to the asymptotic “true” half-life
N
= 1 /
s
. Thus, when we're
given a vector
v
of values
e
t
indexed by days
t
, we do something like
this:
true_N = N
this_N_est = 1.0
this_E = 0.0
for e_t in v:
this_E = this_E * (1-1/this_N_est) + e_t * (1/this_N_est)
this_N_est = this_N_est*(1-1/true_N) + N * (1/true_N)
The Financial Modeling Feedback Loop
One thing any quantitative person or data scientist needs to under‐
stand about financial modeling is that there's a feedback loop. If you
find a way to make money, it eventually goes away—sometimes people
refer to this as the fact that the market “learns over time.”
One way to see this is that, in the end, your model comes down to
knowing some price (say) is going to go up in the future, so you buy
it before it goes up, you wait, and then you sell it at a profit. But if you
think about it, your buying it has actually changed the process, through
your market impact, and decreased the signal you were anticipating.
Of course, if you only buy one share in anticipation of the increase,
your impact is minimal. But if your algorithm works really well, you
tend to bet more and more, having a larger and larger impact. Indeed,
why would you
not
bet more? You wouldn't. After a while you'd learn
the optimal amount you can bet and still make good money, and that
optimal amount
is
large enough to have a big impact on the market.
That's how the market learns—it's a combination of a bunch of algo‐
rithms anticipating things and making them go away.
