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Total Posts: 1143
Joined: Jun 2005
Posted: 2019-11-24 16:19
- Index is calculated over several prices (contributors). Let their number be N.
- Time to time, a feed from a contributor interrupts. N ->N-1
- Index is taken as an estimator over available price sample

I compared
- mean,
- weighted mean with exponential weight (wi~exp(-abs(E[x]-xi))), and
- trimmed mean.

While mean is efficient estimator, trimmed mean is less sensitive to feed interruption and weighted mean performs best only when extreme points disappear.

Do you know any better estimator than trimmed mean?
Interruption is "a matter of life" and is unavoidable


Total Posts: 68
Joined: Nov 2009
Posted: 2019-11-28 12:54
Few thoughts:

- how do you measure estimator performance? Can you back-fill the feed ex-post and compare estimates with true values?

- I would normally try to estimate the missing contributor from available information, ideally from the other contributors.


Total Posts: 1143
Joined: Jun 2005
Posted: 2019-11-28 13:30
It is not about "contributors" to the index, but imagine 20 different sources publishing the same thing from different geo-locations.

I don't like an idea of back fill, but, yes, historical data collected by trading bot show beautiful backtesting results.

> estimate the missing contributor

Good idea, thank you. I have all I need. This one is actually obvious, I was blinded.

PS. However, initial question remains - what is the best measure for the mean (index) with changing contributors?
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