Outliers and Robust Statistics

An outlier is a value far from the rest of the data. In trading, outliers come in two kinds: errors, such as a bad tick that prints a price 50% away from the market, and genuine extreme events, such as a crash day or a takeover jump. Errors should be fixed or removed; genuine extremes often matter most for risk and must be kept. Robust statistics are methods that are less sensitive to outliers, helping researchers see the typical pattern without letting a few values dominate.

How outliers distort common statistics#

Detecting outliers#

The standard z score method is itself distorted by outliers, since the mean and standard deviation include them. Robust z scores avoid this.

Robust measures#

MAD = median(|x - median(x)|)
robust standard deviation ≈ 1.4826 × MAD   (for normal data)

Other robust tools:

• Trimmed mean: drop a percentage of the highest and lowest values, then average.
• Winsorising: cap extreme values at chosen percentiles, such as the 1st and 99th.
• Rank based methods: Spearman correlation, rank transformed signals.
• Robust regression: methods such as Huber regression that reduce outliers' influence.

Winsorising signals in quant research#

Quantitative strategies often winsorise or rank signals across stocks before combining them. For example, a company with a tiny positive earnings figure might show a P/E of 5,000, which would dominate a raw value signal. Capping extremes or using ranks keeps a few companies from distorting the portfolio. See Combining Signals and Factor Investing Explained.

When outliers are the point#

In risk management, extreme values are not noise to be removed; they are the main concern. Tail events drive drawdowns, margin calls and ruin. Removing genuine crash days from a backtest makes a strategy look far safer than it is. See Fat Tails and Maximum Drawdown.

Practical guidelines#

1. Separate errors from genuine events using domain knowledge and multiple data sources.
2. Fix or remove errors; keep genuine extremes for risk analysis.
3. Use robust measures for signals and typical behaviour.
4. Report sensitivity: show results with and without extreme values.
5. Document every adjustment to keep research reproducible. See Backtest Reproducibility.

Frequently asked questions#

What is an outlier in trading data?#

A value far from the rest of the data, caused either by a data error or by a genuine extreme market event.

What are robust statistics?#

Statistical methods, such as the median and median absolute deviation, that are less affected by outliers than the mean and standard deviation.

Should I remove outliers from a backtest?#

Remove data errors, but keep genuine extreme events, since they are often the most important for understanding risk.

Next, learn what makes a result convincing in Statistical Significance in Trading.