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Periodogram

A graphical plot with abscissa given by the number p of consecutive numbers constituting a single period and ordinate given by the correlation ratio eta. The equation of the periodogram is

eta^2=((a^2)/(2m^2)sin^2((mpip)/T)+(sigma_b^2)/m)/(1/2a^2+sigma_b^2),

where each of the terms of the sequence u_x consists of a simple periodic part of period T, together with a part which does not involve this periodicity b_x, so

u_x=asin((2pix)/T)+b_x,

sigma_b is the standard deviation of the bs, sigma is the standard deviation of the us, and m is the number of periods covered by the observations.

See also

Time Series Analysis

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References

Schuster. Terrestrial Magnetism 3, 24, 1898.Whittaker, E. T. and Robinson, G. "The Periodogram in the Neighbourhood of a True Period" and "An Example of Periodogram Analysis." §174-175 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 346-362, 1967.

Referenced on Wolfram|Alpha

Periodogram

Cite this as:

Weisstein, Eric W. "Periodogram." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Periodogram.html

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