Forecasting the Sunspot Cycle

Abstract

Read before the ROYAL STATISTICAL SOCIETY on Wednesday, May 18th, 1977, the President, Miss STELLA V. CUNLIFFE in the Chair] SUMMARYThe problem of forecasting the development of the well-known sunspot cycle of approximately 11 years from observations made early in the cycle is considered. Each cycle is described by a member of a family of curves with different parameters for each cycle. Forecasts are obtained using this model and these forecasts are combined with forecasts obtained from an autoregressive model. Forecasting the time of maximum sunspot activity and the maximum sunspot number is also discussed.

State space modeling of Gegenbauer processes with long memory

“…From the results of Table 17 it is clear that the forecast model presented in this paper performs better than the AR model introduced in Morris (1977) in terms of the forecast mean square errors ranging from 3 to 5 step ahead predictions. In his paper it is acknowledged that the utilized traditional AR model up to 30 lags does not yield satisfactory forecast MSE's.…”

“…It yielded mean square forecast errors that were better up to the five step ahead forecast than the values given in Morris (1977) for the same series using a similar forecasting technique. In Table 17 the comparative results of the MSE values beginning at the third step ahead forecast beyond the minimum year of a sunspot cycle is recorded, since Morris (1977) begins the assessment at the same evaluation point.…”

“…It yielded mean square forecast errors that were better up to the five step ahead forecast than the values given in Morris (1977) for the same series using a similar forecasting technique. In Table 17 the comparative results of the MSE values beginning at the third step ahead forecast beyond the minimum year of a sunspot cycle is recorded, since Morris (1977) begins the assessment at the same evaluation point. To further illustrate the forecasting efficiency of the method proposed in this paper, a comparative evaluation was made with respect to the results provided in Zhang (2003) and Bijari and Khashei (2011) with respect to Wolfer's sunspots by utilizing the same data and are shown below in Table 18.…”

A bayesian approach to modelling stochastic cycles

“…This series has been studied and modelled by many authors. (Morris, 1977, gives a detailed review of these models). In almost all of them it is generally accepted that the series possesses a periodical movement or cycle, whose period oscillates between 9 and 14 years, with an average value of 11 years.…”

‘Skinning a cat’: alternative models of representing temperature trends

“…The most famous of these series is undoubtedly the sunspot index, first investigated empirically by Newcomb (1901) and then by Schuster (1906) using periodogram analysis, a technique that was extended by Larmor and Yamaga (1917). Yule (1927) later used the series to illustrate his autoregressive scheme, which was subsequently generalised nonlinearly by Moran (1954): later contributions to the modelling and prediction of the sunspot index have been provided by, for example, Granger (1957), Craddock (1967), Morris (1977) and Yoon (2006). Consistent with this historical perspective, over the last decade I myself have analysed various temperature series using a variety of statistical models, usually with the aim of extracting the trend component.…”