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Interpreting Super-White Stock Return Spectra

Article Quant Q&A · Author: Barnaby
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Summary

The document discusses a claim that stock and index return spectra became unusually uniform after the late 1970s. Standard frequency-domain tests, which look for sinusoidal components with unusually large amplitudes, reportedly found few departures from white noise; the cited work describes amplitudes as even more uniform than white noise would suggest. The proposed interpretation is that trading activity may reduce detectable patterns beyond ordinary market efficiency, though the post raises this as a question rather than establishing a mechanism.

The excerpt offers no detailed dataset, test specification, or causal evidence explaining the claimed super-whiteness. A reply challenges the interpretation, pointing out that white noise itself is random and asking why greater uniformity could not arise by chance. The discussion therefore highlights a distinction between failing to reject a white-noise null and proving that returns follow a special predictable process. The result is limited to the cited analysis and its frequency-domain tests; it does not establish that all stocks or indexes lack exploitable signals.

Key ideas

  • The cited paper reports that standard tests found fewer detectable spectral departures in stock returns after the late 1970s.
  • The discussion describes unusually uniform return-spectrum amplitudes as super-whiteness.
  • The post speculates that trading activity could create this pattern but supplies no causal model.
  • Failure to reject a white-noise null does not prove that returns are exactly white noise.
  • The reply questions whether the reported uniformity exceeds what random variation could produce.

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EquitiesStatisticsUS markets
Full text
# Are all stocks and stock indexes just white noise


# Are all stocks and stock indexes just white noise












In the paper Super-Whiteness of Returns Spectra from Erhard Reschenhofer of University of Vienna it is commented the following

"Until the late 70’s the spectral densities of stock returns and stock index returns exhibited a type of non-constancy that could be detected by standard tests for white noise. Since then these tests have been unable to find any substantial deviations from whiteness in stocks returns and index returns.

Actually, there is a striking power deficiency, which implies that these series exhibit even fewer patterns than white noise. A typical frequency domain test for white noise rejects the null hypothesis whenever the time series contains sinusoidal components with too large amplitudes.

Under the null hypothesis of white noise, all amplitudes are roughly of the same size, no amplitudes can be systematically larger than others. There is a perfect uniformity. Amazingly, the amplitudes obtained from the S&P 500 returns appear even more uniform. This super-whiteness can not just be the result of random fluctuations. Something more must be at work besides chance.

All in all, it seems that active traders contribute to market efficiency only up to a certain point. Beyond that point, their activities may lead to super-efficiency, which must on no account be misinterpreted as perfect efficiency but rather implies some special form of predictability."

This paper seems to imply that a portfolio should be taken as just white noise or better super white noise so basically there is no signal or if there is must be microcopic in power and that this super white noise must be a mix of superpossitioned different distribution white noises with additional noise components as to lead to this greater uniformity in amplitude than white noise.

If you have any additional information on what processes could create this superwhite noise kindly let me know.

EDIT

Power deficiency of significance of tests on the frequency domain for rolling windons of 5 years found after the 70s (data analyzed from the 50s). This significance results of tests with much lower rates than the rejection level of the null hipothesis implies that any deviation from the null hypothesis reveals that the spectrum should be greater at some frequencies and lower at others.

## Answer by Andrew (score 1)

https://quant.stackexchange.com/a/18973

First. Use quotes around the quoted part of this question to make it clear what isn't your opinion.

Second. White noise is exactly what efficiency should generate. This para. neither makes sense nor is supported (if the support is elsewhere in the quoted article please post it). My questions in parentheses prefaced with "AC":

"Under the null hypothesis of white noise, all amplitudes are roughly of the same size, no amplitudes can be systematically larger than others. There is a perfect uniformity. Amazingly, the amplitudes obtained from the S&P 500 returns appear even more uniform (AC: explain. White noise is defined as mean-variance stationary IID). This super-whiteness can not just be the result of random fluctuations (AC: why not? White noise would appear to be defined as random fluctuations). Something more must be at work besides chance. (AC: ?)"

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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