An Experiment in the Anaysis and Prediction of Time Series

Craddock, J. M.

doi:10.2307/2986719

Cited by 9 publications

(3 citation statements)

References 2 publications

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“…Considerable research has been directed towards the analysis of this series in the literature. For example, Yule (1927), Moran (1954), Craddock (1967), Box and Jekins (1970), Brillinger and Rosenblatt (1967), Morris (1977), Olvera (2005) and Gil‐Alana (2009) and many others have studied these data.…”

Section: Reanalysis Of the Monthly Sunspot Series: 1749‐2009mentioning

confidence: 99%

Overlapped grouping periodogram test for detecting multiple hidden periodicities in mixed spectra

Wen

2011

Journal Time Series Analysis

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Hidden periodicity is a featured phenomenon in many area of the real world, for example, in astronomy and climatology. Under white noise assumption, the problem of searching for hidden periodicity has been studied extensively in the literature. However, under mixed spectra, especially when compound periodicities are involved, most of the existing methods lose their efficiencies. An overlapped grouping periodogram (OGP) test is proposed in this paper to detect multiple hidden periodicities in mixed spectra. Its test statistic is proven to converge to Fisher's g-statistic almost surely. Difficulties arising from the implementation of the OGP test are tackled and an empirical data-adaptive confidence interval for grouping parameter selection is constructed when red noise is assumed. The large sample properties of the proposed OGP test are studied via Monte Carlo simulations, and the power of the test is further illustrated by applying it to the reanalysis of the monthly international sunspot series. By employing the new method, a 10-year cycle and a 11-year cycle are detected respectively in the monthly international sunspot series. These two cycles combined to form a super cycle with a period of about 110 years for the updated estimate to the solar cycle. The goodness of the OGP fit to the sunspot series is examined.

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Section: Reanalysis Of the Monthly Sunspot Series: 1749‐2009mentioning

confidence: 99%

Overlapped grouping periodogram test for detecting multiple hidden periodicities in mixed spectra

Wen

2011

Journal Time Series Analysis

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“…while appearing to describe the series quite well, did not yield satisfactory forecasts. Moran had considered models up to p = 5 but Craddock (1967) considered models up to p = 30 and using the annual means from 1700 to 1965 obtained the residual variance as a percentage of the variance of the series. This was about 19 per cent for p = 2 up to P = 5, then falling to about 15 per cent at p = 9 and changing very little afterwards.…”

Section: Forecasting the Sunspot Cyclementioning

confidence: 99%

Forecasting the Sunspot Cycle

Morris¹

1977

Journal of the Royal Statistical Society. Series A (General)

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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.

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“…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.…”

Section: Introductionmentioning

confidence: 98%

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

Mills

2010

Climatic Change

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An Experiment in the Anaysis and Prediction of Time Series

Cited by 9 publications

References 2 publications

Overlapped grouping periodogram test for detecting multiple hidden periodicities in mixed spectra

Overlapped grouping periodogram test for detecting multiple hidden periodicities in mixed spectra

Forecasting the Sunspot Cycle

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

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