HotWhopper recently blogged about my post published on WattsUpWithThat?

Much if the critique (and I use the term advisedly) relates to this paragraph from the original post:

 Unfortunately, the analysis is of no value because, as is commonly known, the CPA cannot be used on auto-regressive time series. This can be easily demonstrated. Here’s a random sample of an ARIMA[3,1,1] process (This is not to infer the climate can be modeled as an ARIMA process. CPA fails for any integrative process, a class which in all likelihood the climate falls within.

Laughingly, the author uses this animation to complain the the output of AIRMA process sample doesn’t look like the GISS data.

 But compare that to the GISTemp chart above. They are nothing alike.

That’s a lot of ignorance to pack into one sentence. Leaving aside the fact that the GISS plot is filtered (looks like yearly mean data to me, perhaps with MA filtering) while the ARIMA plot represents raw monthly samples, the point of using a statistical models is not to generate data that matches the temperature record but to model the statistics. (Hint: that’s why they call it a statistical model.) Here we are using it to show why changepoint analysis is an inappropriate tool for examining climate data. If CPA fails for a simple ARIMA process (and it does), then it is certainly no match for climate dynamics which contain, off the top of my head, at least five cumulative sub-processes (ocean, atmosphere, glaciers, carbon sink, sea ice, etc.) which are all non-linearly cross-coupled to boot!

As I mentioned in the original post, a simple ARIMA process generator cannot match the dynamics of such a complex system but it is sufficient to show the pitfalls of naively applying CPA to feedback processes whose output depends in some way on its accumulated past history.  Such systems when subjected to random fluctuations, either from external forcing or generated internally, are known to exhibit rapid phase transitions (as shown in the ARIMA plot e.g. between “month” 800 and 1500). CPA mistakenly interprets these phase transition regions as forcing changepoints when none exists, and misses real forcing changepoints which can be masked by the internally generated phase transitions. It’s not magic Sou, it dynamics. I refer you to any introductory text on the subject.

I have not come across any other article anywhere that states that you cannot apply change point analysis if there is any autoregression in the time series. I did find an article describing a technique to distinguish between shifts in the mean and autocorrelation.

This one’s a hoot. The article Sou linked to is about testing for auto-regression so one can determine if CPA results can be trusted! Quoting from the article,

The pattern test can be used to detect a violation of the assumption of independent errors when control charting data and performing a change-point analysis.

It is clear Sou doesn’t understand the subject matter she’s commenting on so here’s a helpful hint. Auto-regression makes the time samples interdependent which violates the assumption underling changepoint analysis (independent samples), precisely the point I made in the WUWT article.

The author of the above paper has an excellent introduction to changepoint analysis here. Here’s a quote from that text:

It is assumed that the ei are independent with means of zero.  Taylor (2000b) provides a procedure for detecting a departure from this assumption.  Data not appropriate for a change-point analysis and control charting include autoregressive time series data such as stock prices.

And then there is this gem

I don’t know how many runs Jeff had to do to get so much of the chart above the zero line, but it strikes me that if he could have got a run anything like the actual surface temperature charts he would have used it. And if he did find one that looked anything like the surface temperature chart, would he have said how many runs he had to do to get it? Would he have computed the odds? Maybe, maybe not. The odds would have been very low. I haven’t done it myself but if anyone has, do tell.

As if the offset has anything to do with analyzing anomaly data. And again Sou exhibits the fundamental misunderstanding that somehow the point of the exercise is to generate a series that “looked anything like the surface temperature chart”.

Next exhibit:

First he argues that there has been a rise in global surface temperature, a “warming trend” that has “remained constant” at around 0.008°C/decade2.  He’d be wrong about that. Global surface temperatures have risen around 0.8°C since the 1920-30s. Since 1950, the global surface temperature has risen by an average of 0.122°C a decade. Since 1980 it has risen by 0.156°C a decade. It’s not had a constant rate of increase of 0.008°C per decade2 (nor a constant increase of 0.08°C a decade).

Again the author reiterates my point illustrated in the plot below from the original post:

The slope is in constant flux between roughly the limits described in the quote above. As such, the only meaningful metric is the trend of the trend, (the slope of the dotted line), which has stayed constant at 0.008°C/decade2 for the entirety of the record. Perhaps Sou wants to see some fingerprint of man’s influence in the plot above but there is none to be had.

The leap of faith is that according to Jeff, this large rise in surface temperature must be being caused by something other than human actions. Magic? If it were random, then temperatures would have gone up and down but on balance not moved far from a mean.

A glance at the paleoclimate plot below should disabuse anyone of the notion that the mean climate has meaning, or at least that we should pray we never live to see it.

Does the author truly believe that our climate is not subject to large and persistent natural variation? If so, she is at odds with the climatologists she holds in such esteem. Here’s a recent example from a paper (Atmospheric controls on northeast Pacific temperature variability and change, 1900–2012) published in the Proceedings of the National Academy of Sciences by Johnstone and Mantua (2014) (emphasis mine)

This study uses several independent data sources to demonstrate that century-long warming around the northeast Pacific margins, like multidecadal variability, can be primarily attributed to changes in atmospheric circulation. It presents a significant reinterpretation of the region’s recent climate change origins, showing that atmospheric conditions have changed substantially over the last century, that these changes are not likely related to historical anthropogenic and natural radiative forcing, and that dynamical mechanisms of interannual and multidecadal temperature variability can also apply to observed century-long trends.

Again, Sou no magic, just dynamics. Pick up a book on the subject.

Note: At the risk of appearing to join Sou in her haughty, gratuitous aspersion of process/production engineers, for the record I am a research engineer with 35 years experience. I hold seven patents in the fields of signal processing, non-linear dynamics and modeling.

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