VII. On a method of investigating periodicities disturbed series, with special reference to Wolfer's sunspot numbers

Abstract

VII. On a Method o f Investigating Periodicities Disturbed Series, ivith reference to W o l f e d sS unspot Numbers.

Perspectives on system identification

“…Econometrics has a long tradition of giving inspiration to time series and difference equation modeling and its roots coincide with developments in statistics. The work on time series dates back to Jevons (1884), Yule (1927), and Wold (1938). The classic paper Mann and Wald (1943) developed the asymptotic theory for the LS estimator for stochastic linear difference equations (AR systems).…”

A Comparative Study of the Effectiveness of Adaptive Filter Algorithms, Spectral Kurtosis and Linear Prediction in Detection of a Naturally Degraded Bearing in a Gearbox

“…Models which use the information from only the past system outputs are called all-pole or autoregressive models, and were first used by Yule [37] in an investigation of sunspot numbers. In Linear Prediction the objective is to predict or estimate the future output of a system based on the past output observations.…”

Predictability of the Earth’s polar motion

“…It is well-known that a pure sinusoidal function can be represented as a second-order AR time series [see e.g. Yule, 1927]. In fact, it can be shown that a linear combination of K complex sinusoids (with exponentially decaying or growing amplitudes) can be expressed as a 2Kth order AR time series, and the K complex periods are related to the 2K (real) AR coefficients through the Prony's relation [for details see Chao & Gilbert, 1980;Chao, 1984].…”

“…However, the Earth's meteorological transfer function being intricate and non-linear, it is only natural that the annual wobble thereby generated will have an amplitude that varies from year to year and a period that fluctuates about the driving period 365.25 days. the "disturbed pendulum" model of Yule [ 1927]; for the modulating effects of multiple periods on the instantaneous period and amplitude of the polar motion, see Chao [1983]. )…”