# Robust outlier detection in financial timeseries

I'm looking for some robust techniques to remove outliers and errors (whatever the cause) from financial time-series data (i.e. tickdata).

Tick-by-tick financial time-series data is very messy. It contains huge (time) gaps when the exchange is closed, and make huge jumps when the exchange opens again. When the exchange is open, all kinds of factors introduce trades at price levels that are wrong (they did not occur) and/or not representative of the market (a spike because of an incorrectly entered bid or ask price for example). This paper by tickdata.com (PDF) does a good job of outlining the problem, but offers few concrete solutions.

Most papers I can find online that mention this problem either ignore it (the tickdata is assumed filtered) or include the filtering as part of some huge trading model which hides any useful filtering steps.

Is anybody aware of more in-depth work in this area?

Update: this questions seems similar on the surface but:

• Financial time series is (at least at the tick level) non-periodic.
• The opening effect is a big issue because you can't simply use the last day's data as initialisation even though you'd really like to (because otherwise you have nothing). External events might cause the new day's opening to differ dramatically both in absolute level, and in volatility from the previous day.
• Wildly irregular frequency of incoming data. Near open and close of the day the amount of datapoints/second can be 10 times higher than the average during the day. The other question deals with regularly sampled data.
• The "outliers" in financial data exhibit some specific patterns that could be detected with specific techniques not applicable in other domains and I'm -in part- looking for those specific techniques.
• In more extreme cases (e.g. the flash crash) the outliers might amount to more than 75% of the data over longer intervals (> 10 minutes). In addition, the (high) frequency of incoming data contains some information about the outlier aspect of the situation.
• I don't think this is a duplicate because of the nature of the data. The problem discussed on the other question concerned regularly observed time series with occasional outliers (at least that's how I interpreted it). The nature of tick-by-tick data would lead to different solutions due to the exchange opening effect. – Rob Hyndman Aug 4 '10 at 10:09
• possible duplicate of Simple algorithm for online outlier detection of a generic time series This question is proposed to be closed as a duplicate. Could you please let us know at the meta thread if and how your context is different from the question I linked? – user28 Aug 4 '10 at 10:10
• @Rob But the exchange opening effect only determines when you have to run the algorithm. The fundamental issue remains the same. Even in network data you have the 'office opening effect' where traffic peaks as soon as an office opens. At the very least, the OP should link to that question, scan the answers there and explain why the solutions there do not work so that a suitable answer can be posted for this question. – user28 Aug 4 '10 at 10:12
• I agree with @Rob. This kind of data can pose unique challanges, so this is not a duplicate. – Shane Aug 4 '10 at 10:46
• I think it belongs here. The question is about analyzing irregularly spaced, very noisy time series. Have you had a look at "An Introduction to High-Frequency Finance" by Dacorogna, Olsen and a bunch of others? Or the papers by the same authors? – PeterR Aug 4 '10 at 12:30

The problem is definitely hard.

Mechanical rules like the +/- N1 times standard deviations, or +/ N2 times MAD, or +/- N3 IQR or ... will fail because there are always some series that are different as for example:

• fixings like interbank rate may be constant for some time and then jump all of a sudden
• similarly for e.g. certain foreign exchanges coming off a peg
• certain instrument are implicitly spreads; these may be near zero for periods and all of a sudden jump manifold

Been there, done that, ... in a previous job. You could try to bracket each series using arbitrage relations ships (e.g. assuming USD/EUR and EUR/JPY are presumed good, you can work out bands around what USD/JPY should be; likewise for derivatives off an underlying etc pp.

Commercial data vendors expand some effort on this, and those of use who are clients of theirs know ... it still does not exclude errors.

• +1 yes, nothing is perfect. Tickdata.com (whose paper is mentioned) also includes outliers and they also strip out too much good data (when compared with another source). Olsen's data is close to being terrible, and I generally just indicative. There's a reason that banks pay big operations teams to work on this. – Shane Aug 4 '10 at 16:10
• I like your idea about using known arbitrage relations. have you tried this at all in your previous job? – jilles de wit Aug 5 '10 at 7:27
• No, we never fully formalized that. But I think we used some simple ones (ie ETF vs underlying index etc). It's been a few years though. – Dirk Eddelbuettel Aug 5 '10 at 11:43

I'll add some paper references when I'm back at a computer, but here are some simple suggestions:

Definitely start by working with returns. This is critical to deal with the irregular spacing where you can naturally get big price gaps (especially around weekends). Then you can apply a simple filter to remove returns well outside the norm (eg. vs a high number of standard deviations). The returns will adjust to the new absolute level so large real changes will result in the loss of only one tick. I suggest using a two-pass filter with returns taken from 1 step and n steps to deal with clusters of outliers.

Edit 1: Regarding the usage of prices rather than returns: asset prices tend to not be stationary, so IMO that can pose some additional challenges. To account for the irregularity and power law effects, I would advise some kind of adjustment if you want to include them in your filter. You can scale the price changes by the time interval or by volatility. You can refer to the "realized volatility" literture for some discussion on this. Also discussed in Dacorogna et. al.

To account for the changes in volatility, you might try basing your volatility calculation from the same time of the day over the past week (using the seasonality).

• By using only the returns you become very vulnerable to ladders (i.e. a sequence of prices that climbs or drops away from the norm, where each individual return is acceptable, but as a group they represent an outlier). Ideally you'd use both the return and the absolute level. – jilles de wit Aug 4 '10 at 14:01

You can address the problem of time varying volatility with the robust statistics framework. This is done by using a robust estimator of the conditional variance (instead of the robust estimator of the unconditional variance I was suggesting earlier): the M-estimation of the GARCH model. Then you will have a robust, time varying estimate of $(\hat{\mu}_t,\hat{\sigma}_t)$ which are not the same as those produced by the usual GARCH fit. In particular, they are not driven by a few far away outliers. Because these estimate are not driven by them, you can use them to reliably flag the outliers using the historical distribution of the
$$\frac{x_t-\hat{\mu}_t}{\hat{\sigma}_t}$$