Fourier Covariance Estimation and Minute-Return Realized Variance

Summary

The document raises a comparison between a Fourier-based estimator of realized variance and covariance and the conventional sum of squared returns. The author applies the estimator to one day of ultra-high-frequency observations, samples the data at one-minute intervals, and truncates the frequency expansion after a chosen cutoff. The central question is whether this procedure still estimates daily realized variance and whether its output should agree with the minute-return sum.

No answer or estimator derivation is included, so the text does not establish equivalence or quantify the effects of sampling and frequency truncation. Those choices matter to interpretation: the Fourier calculation is based on a frequency representation, while summing squared sampled returns gives a realized measure at the chosen sampling interval. A useful comparison would need the estimator’s precise definition, sampling scheme, cutoff behavior, and assumptions about microstructure noise and the underlying price process.

Key ideas

• The author asks whether a truncated Fourier estimator on sampled observations represents daily realized variance.
• The proposed benchmark is the sum of squared returns at the same sampling interval.
• Frequency truncation and sampling choices may affect comparability between the two measures.
• The document poses the methodological question but supplies no derivation or conclusion.

Tags

# Fourier transform covariance estimator


# Fourier transform covariance estimator












I am estimating realized variance and covariance by the estimator described in this paper, and relying on Fourier Transform.

Now, as my data is one day of data in ultra high frequency, so that the estimation takes time, I sample the data every minute but still use that estimator, cutting the frequencies after 100.

I have some confusion : can you confirm that by applying that paper I am calculating the daily realized variance, and that the result should be comparable to what I find if I simply sum the squared minute returns for the day?

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