Statistics Heresy

Statistics is an analytical tool not a rhetorical device

Statistical analysis of two climate time series

by John Reid

Unlike the variance density spectral estimate or `power spectrum', the sample periodogram is a rigorously defined statistic and, as such, can be used to distinguish between deterministic cycles and stochastic processes in a given time series. Under the null hypothesis, whereby the time series is assumed to be white, the periodogram ordinates are independent and identically distributed and, when normalized, have a chi-squared distribution with two degrees of freedom. This facilitates the testing for significance of both non-white trends and individual spectral peaks. Here we examine two climate time series: the EPICA Dome C Deuterium ice core time series from 490 kyr to the present and the GISS time series of annual global average surface temperature from 1880 to 2014. The EPICA time series showed significant peaks at 41.0 and 23.3 kyr indicating the presence of deterministic cycles with periods close to the periods of obliquity and precession of the Earth's orbit. On the other hand the GISS time series showed no evidence of decadal or multidecadal cycles and is well described by a purely stochastic ARIMA(0,1,1) model. Neither was there evidence of a deterministic trend in the GISS data, the apparent trend being attributable to spurious regression.

Posted: 30 January 2016

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Deterministic cycles and random excursions

by John Reid

Random walks are the outcome of a summing or integrating process and as such are widespread in nature. They are manifested as power law relationships between variance density and frequency. The random walk effect may be removed by differencing and decimating the data. In this way it is possible to show that apparently deterministic cycles observed in some natural time series are, in fact, random walk excursions.

Posted: 9 September 2015

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