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Approaches to Adding Synthetic Microstructure Noise to Prices

Article Quant Q&A · Author: barrymac
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Summary

The document discusses ways to add realistic-looking microstructure variation to a price series while preserving its broader directional signal. One suggestion interpolates between the current price and a future price over a chosen horizon, with the interpolation fraction perturbed by zero-mean Gaussian noise. This approach depends on future information, so it is suitable only for applications where lookahead is acceptable, such as offline visualization or simulation; it would not be valid as a real-time signal construction method.

Other proposals include modifying higher-frequency components in a Fourier representation, or sampling deviations between a fair-value model and observed prices. These ideas are brief suggestions rather than a standardized recipe or a comparison backed by experiments. The document does not specify how to calibrate noise distributions, select frequencies or horizons, or validate that synthetic prices reproduce actual market microstructure. Any generated series would therefore need separate checks for realism and for preserving the intended aggregate movement.

Key ideas

  • A noisy interpolation between current and future prices can create variation around a directional path.
  • Using a future price introduces lookahead and limits the method to settings where that is acceptable.
  • Fourier-domain changes to higher-frequency components are proposed as another way to add noise.
  • Residuals from a fair-value model can be sampled to perturb prices.
  • The suggestions lack calibration details and empirical validation.

Tags

Market microstructureStatisticsBacktesting
Full text
# Are there any standard techniques for adding realistic synthetic microstructure noise to a price series?


# Are there any standard techniques for adding realistic synthetic microstructure noise to a price series?












This may seem like a strange question, but for my particular application we need to actually add synthetic microstructure noise to real time charts. The signal should still be representative of the aggregate market direction.

I expect that a good technique would be something related to signal processing in electronics or sound engineering. They have white noise generators that can be restricted to a band. I would rather something far less complicated though.

Is it perhaps good enough to take a random percentage of the actual change from the last difference?

## Answer by Serg (score 3)

https://quant.stackexchange.com/a/3800

I assume, this is not for real-time display, so you can use the price from future. If this is not the case, this answer is irrelevant.

I don't know about a standard technique, but this is my suggestion:

$p_{noise} = p_{current} + \nu * (p_{future} - p_{current})$

where $p_{future}$ is future price for some horizon, and $\nu$ is a zero-mean Gaussian noise.

## Answer by babelproofreader (score 1)

https://quant.stackexchange.com/a/3801

Maybe the accepted answer to this earlier thread and the more detailed description on my blog might be of use to you. Within the FFT you could just manipulate the higher frequency components to create your synthetic microstructure noise.

## Answer by Kumar (score 0)

https://quant.stackexchange.com/a/3795

Why not use a Fair value model to predict prices and then randomly sample from the difference of the model and actual prices. The errors would be as good as your model

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.