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A Speed-based Estimator of Signal-to-Noise Ratios

Author

Listed:
  • Yuang Song

    (Columbia University)

  • Olympia Hadjiliadis

    (CUNY-Hunter College)

Abstract

We present an innovative method to measure the signal-to-noise ratio (SNR) in a Brownian motion model. That is, the ratio of the mean to the standard deviation of the Brownian motion. Our method is based on the method of moments estimation of the drawdown and drawup speeds in a Brownian motion model, where the drawdown process is defined as the current drop of the process from its running maximum and the drawup process is the current rise of the process above its running minimum. The speed of a drawdown of K units (or a drawup of K units) is then the time between the last maximum (or minimum) of the process and the time the drawdown (or drawup) process hits the threshold K. Our estimator only requires the record values of the process and the times at which deviations from the record values exceed a certain threshold, whereas the uniformly minimum-variance unbiased estimator (UMVUE) requires the entire path of the process. We derive the asymptotic distributions of both estimators and compare them.

Suggested Citation

  • Yuang Song & Olympia Hadjiliadis, 2025. "A Speed-based Estimator of Signal-to-Noise Ratios," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-15, June.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10150-0
    DOI: 10.1007/s11009-025-10150-0
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    References listed on IDEAS

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    1. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    2. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    3. Yang, Dennis & Zhang, Qiang, 2000. "Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices," The Journal of Business, University of Chicago Press, vol. 73(3), pages 477-491, July.
    4. Hongzhong Zhang & Olympia Hadjiliadis, 2012. "Drawdowns and the Speed of Market Crash," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 739-752, September.
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