Let’s look again at what Rasmus was saying before Gavin sent him to the end of the bench. He argued that Cohn and Lins were sucking and blowing by calibrating the autocorrelation on instrumental records, which themselves contained a trend. Gavin endorsed this position. On the face of it, this seems like a plausible criticism. However, this is not what Cohn and Lins either did or said. (One of the irritating features of realclimate authors is that they seldom quote directly from their adversaries and frequently set up straw men. You always have to check their characterizations. I try to avoid the same problem by quoting extensively as much as possible.)
Here is Rasmus arguing against using instrumental records to provide a benchmark long-term persistence for null distributions:
When ARIMA-type models are calibrated on empirical data to provide a null-distribution which is used to test the same data, then the design of the test is likely to be seriously flawed. To re-iterate, since the question is whether the observed trend is significant or not, we cannot derive a null-distribution using statistical models trained on the same data that contain the trend we want to assess. Hence, the use of GCMs, which both incorporates the physics, as well as not being prone to circular logic is the appropriate choice.
I do not believe that statistical models are appropriate because i: they are used to test a null-hypothesis where no antropogenic forcing (of just solar volcanoes) is assumed, ii) they are trained on empirical data subject to forcings (be it anthopogenic as well as solar/volcanic)
So I think that I’ve characterized Rasmus fairly. Now let’s see Gavin’s endorsement of this position:
It may help you to follow if you actually read what is said. …Why you appear to think that GCMs should not be tested against the real world is beyond me.
Oops, that was Gavin being snarky to a civilian. People complain about me being sarcastic, but how often have I been snarky with a civilian? Not very often. OK occasionally with Lambert, who’s hardly a civilian, but not with Dano who was always civil here. Also I hope that there’s a difference in tone – I like to think that I’m ironic as opposed to merely bitchy.) Be that as it may, here’s Gavin on the same issue:
Maybe I can interject. First, I think we really all agree that statistics and physics are both useful in this endeavour. The ‘problem’ such as it is with Cohn and Lins conclusions (not their methodology) is the idea that you can derive the LTP behaviour of the unforced system purely from the data. This is not the case, since the observed data clearly contain signals of both natural and anthropogenic forcings. Those forcings inter alia impart LTP into the data. The models’ attribution of the trends to the forcings depends not on the observed LTP, but on the ‘background’ LTP (in the unforced system). Rasmus’ point is that the best estimate of that is probably from a physically-based model – which nonetheless needs to be validated. That validation can come from comparing the LTP behaviour in models with forcing and the observations. Judging from preliminary analyses of the IPCC AR4 models (Stone et al, op cit), the data and models seem to have similar power law behaviour, but obviously more work is needed to assess that in greater detail. What is not a good idea is to use the observed data (with the 20th Century trends) to estimate the natural LTP and then calculate the likelhood of the observed trend with the null hypothesis of that LTP structure. This ‘purely statistical’ approach is somewhat circular. Maybe
that is clearer?
So their concern is circularity. Fair enough, although they don’t seem in a big hurry to test for circularity elsewhere. Now let’s see what Cohn and Lins actually said. They do not use instrumental temperature records to benchmark autocorrelation – contrary to the allegations of both Gavin and Rasmus. Did someone once say: "It may help you to follow if you actually read what is said" Just my imagination.
Here’s what Cohn and Lins actually said:
The statistical significance, or p-value, associated with an observed trend, however, is more difficult to assess because it depends on subjective assumptions about the underlying stochastic process [von Storch and Zwiers, 1999; Woodward and Gray, 1993; Weatherhead et al., 1998]. In this paper, we consider the idea introduced by Hurst  and discussed by others [Mandelbrot and Wallis, 1969a; Klemeà'¦à⟬ 1974; Lettenmaier and Burges, 1978; Potter, 1976; Potter and Walker, 1981; Hosking, 1984; Bras and Rodriguez-Iturbe, 1985; Vogel et al., 1998; Koutsoyiannis, 2000] that [hydroclimatological] records are realizations of physical processes whose behavior exhibits long-term persistence (LTP). …The purpose of this paper is not to evaluate claims related to LTP, but rather to explore what LTP, if present, implies about the significance of observed trends.
and again later:
The question remains whether natural [hydroclimatological] processes in fact possess LTP. The idea was introduced more than 50 years ago by Hurst , and has been debated ever since [Mandelbrot and Wallis, 1968; Klemeà'¦à⟬ 1974; Potter and Walker, 1981; Hosking, 1984; Loucks et al., 1981; Koutsoyiannis, 2000, 2003]. Hurst’s fundamental finding has neither been discredited nor universally embraced, but persuasive arguments have been presented (for discussion and additional references, see Koutsoyiannis ). Given the LTP-like patterns we see in longer HC records, however, such as the periods of multidecadal drought that occurred during the past millennium and our planet’s geologic history of ice ages and sea level changes, it might be prudent to assume that HC processes could possess LTP.
As I noted before, the data sets in the original references are long proxy series – not instrumental temperature series. I’m familiar with some, but not all of the Cohn and Lins’ references. Hurst discussed Nile River levels; Mandelbrot and Wallis discussed tree rings, varves, etc. So the issue arises because one sees long-term persistence in proxy records and was not raised because of autocorrelation in instrumental records. So the argument from Gavin and Rasmus is a total red herring. It doesn’t look like Rasmus or Gavin bothered to read the references or even read Cohn and Lins itself very carefully – if you’ll excuse the snark.
Additional to the series mentioned in Cohn and Lins is, of course, the Vostok series, which has pronounced long-term persistence as observed by Pelletier  and discussed here. The Pelletier graph is re-stated here – see the left-hand side of the figure below.
Original Caption: Left: Fig. 1. Power-spectral density estimated with the Lomb periodogram of the temperature inferred from the deuterium concentrations in the Vostok (East Antarctica) ice core. The power-spectral density S is given as a function of frequency for time scales of 500 yr to 200 kyr. Right Fig. 2. Average power-spectral density of 94 complete monthly temperature time series from the data set of Vose et al. (8) plotted as a function of frequency in yr^-1. The power-spectral density S is given as a function of frequency for time scales of 2 months to 100 yr.
While we’re at it, I’d like to draw your attention to a deep-sea proxy series by Carter and Gammon  here , which also shows remarkable long-term persistence and ties in neatly with Vostok. The figure below shows the tie-in between ODP site 1119 and Vostok (see caption for explanation):
Original Caption: Fig.2. Comparison between climate signals from ODP Site 1119 and Vostok, Antarctica, over the last 0.37 My. (A) Insolation curve for latitude 65°N. (B) Deuterium isotope ratio (dD) for the Vostok ice core (15). (C) Natural gamma ray signal from ODP Site 1119 (the scale is reversed) (13). Black triangles indicate age tie points between Site 1119 and Vostok; diamond bullets, the location of warm gamma anomalies in MIS 2 to 3 and 6 (the latter anomaly also occurs in the oxygen isotope record at DSDP Site 594) (17, 18). These features are site-specific and result from seaward movement of the STF and its probable merging with the SAF into an intense combined frontal zone, driven by the lowered sea level at glacial maxima (11). Termination I, III, and IV cold reversals are labeled T-I-cr, T-III-cr, and T-IV-cr, respectively.
Finally, here is a remarkable graphic from Carter and Gammon showing a 3.9 million year proxy. So far, to my knowledge, no one’s analyzed this for long-term persistence, but it would be worth doing. (I might discuss this with Carter who was the first person to encourage my interest in climate.) Carter finds it impossible to distinguish present variability from the variability in his series (C below). All of these series demonstrate long-term persistence and support the validity of the form of inquiry of Cohn and Lins. How one demonstrates significance of present warming as against the variability contained in these proxies is a serious question, which Gavin and Rasmus have not answered. Can a GCM replicate the natural variability of any of these series? Not at 25 model years per calendar day.
Original Caption: Fig.4. Summary history of atmospheric and marine climatic cyclicity over the past 3.9 Ma. (A) Core retrieval from ODP Site 1119 (average recovery, 89%), which controls the completeness of the stable isotope record. (B) Carbon (upper) and oxygen (lower) isotopic measurements for Site 1119C. (C) Natural gamma ray record from ODP Site 1119 (reversed scale), produced by merging onboard MST measurements with downhole log measurements (14). The age scale is derived by matching climatic cycles at the points indicated by crosses to their MIS equivalents at Vostok and at ODP Sites 758 and 1143. Selected isotope stage equivalents are numbered; warm and cold climatic extrema are indicated by W and C above and below the gamma ray curve, respectively; basal triangles indicate incremental 50-m depths on the revised meters composite depth scale (14); and the right-hand scale indicates the possible Antarctic polar plateau air temperature equivalent for Site 1119 cyclicity, based on scaling the amplitude of the MIS 5 to 6 difference to the Vostok and Mt. Fuji deuterium records (15, 22). (D) Sample resolution of gamma ray measurements for Site 1119 (logarithmic scale). MPT, Mid-Pleistocene Transition. (E to G) Benthic oxygen isotope records for the Pacific (Site 1143), Atlantic (Site 659), and Indian (Site 758) oceans, respectively (14).
References: Robert M. Carter* and Paul Gammon, 2004, New Zealand Maritime Glaciation: Millennial-Scale Southern Climate Change Since 3.9 Ma Science 304, 1659 here
Robert M. Carter, C.S. Fulthorpe and H. Lu, 2004. Canterbury Drifts at Ocean Drilling Program Site 1119, New Zealand: Climatic modulation of southwest Pacific intermediate water flows since 3.9 Ma Geology; 32,. 1005–1008; doi: 10.1130/G20783.1; here