Comments on: Mann Sediments and Noise Simulation

By: Replication and due diligence, Wegman style | Deep Climate

Replication and due diligence, Wegman style | Deep Climate — Tue, 16 Nov 2010 07:29:59 +0000

[...] instead of the dubious ARFIMA null proxies, by both the NRC report and Wegman et al. As late as September 2008, McIntyre proclaimed: The hosking.sim algorithm uses the entire ACF and people have worried that this method may have [...]

By: bender

bender — Sun, 28 Sep 2008 22:53:00 +0000

Accumulation of capital is nature’s way of coping with risk inherent in a variable environment. Capital accumulation processes are Hurst process, and many of the processes Mandelbrot studied were capital accumulation processes. Tree growth is a capital acucmulation process. So is stock market growth. That’s why the patterns are everywhere – because capital accumulation is everywhere.

By: Ross McKitrick

Ross McKitrick — Sun, 28 Sep 2008 21:50:49 +0000

#4: It’s true that the OLS normal equations only assume something abuot the residuals; also maximum likelihood assumes normal errors. However Steve is talking about something different. The independent variables cannot be nonstationary in a regression model. The dependent and independent variables have to be I(0), i.e. integrated of order zero. if variables are fractionally or integer-integrated the assumptions that are necessary to use t tables for assessing significance of the slope coefficients no longer hold. If the variables are I(1) the t-states will be wildly misleading unless all the I(1) variables form a linear combination that is I(0), which is called cointegration.

By: Jesper

Jesper — Sun, 28 Sep 2008 21:41:46 +0000

Questions – what is the sampling resolution on the sediment series and ACF plots? You say you compute the ACF out to lag 150, does this mean 150 years?

If these plots show annually-resolved data, presumably these have been interpolated from coarse resolution series, and are somewhat artificial in nature(?) According to the ACF plots, one could presumably obtain quasi-independent data points by using only one of every ~70 values. Of course, this wouldn’t leave you with much to use for calibration with modern temperature records.

By: Frank Scammell

Frank Scammell — Sun, 28 Sep 2008 21:34:30 +0000

Steve, What I find interesting are the models – forward integration, rather than regression. Most of the model results show – more or less positive exponential growth with time. We know (I think) that they throw out all of the model runs that go negative, so you are left with random walks, leading to exponential growth that I have always assumed (but I can’t prove it) are due to roundoff or truncation errors in the model. Aggragating these runs to produce a final result assumes a normal distribution by cherry-picking only positve results.

By: kim

kim — Sun, 28 Sep 2008 14:32:05 +0000

The answer from Kaya, might not work to Maya.
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By: Steve McIntyre

Steve McIntyre — Sun, 28 Sep 2008 14:05:30 +0000

#6. I think that I mentioned a while ago that Mandelbrot himself studied the Hurst parameters of a wide variety of climate time series, including sediments and U.S. tree rings.

By: Steve McIntyre

Steve McIntyre — Sun, 28 Sep 2008 14:04:00 +0000

#4. In this particular example, both situations apply. Consider any temperature history that you can imagine – including any of the Mann 2008 reconstruction variations, together with the implied estimate of various proxies. The residuals are the difference of two very unlike series and, if one of the two series is close to a random walk and one is low order red noise, then the residuals are going to be offside. I thought that this was implicit in how I expressed things, but, if not, that’s surely the case.

By: TAC

TAC — Sun, 28 Sep 2008 10:04:36 +0000

Re: Ross McKitrick (#1),

The only way to justify using the series in a regression model without a transformation to make it stationary...

One of the odd things about the time series that Steve is talking about (which exhibit d=0.50-\epsilon) is that they appear to correspond to stationary ARFIMA models -- but just barely. Why Mother Nature chooses to reside right there is a good question. I look to Koutsoyiannis...

By: John Baltutis

John Baltutis — Sun, 28 Sep 2008 07:45:39 +0000

Re: Ignatus (#4),

Hmmm! According to http://www.uoregon.edu/~robinh/gnmd03_basics.txt linear regression and ANOVA models are those which assume independent and normally-distributed random variables with constant variance. Maybe you’re thinking of generalized linear models (GLMs) that exist for regression-like modeling of data which do not assume a normal distribution.