no attempt to actually address the questions

Under the circumstances, it is curious that he decided to respond at all.

]]>BTW, I wonder if Dr. Junkes himself actually composed the responses. When he was here he was fairly responsive, if a bit pompous.

I don’t think he was responsive then or now.

]]>]]>This problem was recognized almost 80 years ago by Yule (1926) and has been ex-tensively analysed in areas, such as econometrics, where trend time series are the rule.

The present manuscript by Bürger and Cubasch is focused on the problem of attaching physical significance to statistical relationships derived from non-stationary timeseries. This problem was recognized almost 80 years ago by Yule (1926) and has been extensively analysed in areas, such as econometrics, where trend time series are the rule.

For instance, the introduction of a paper written by one of the best known authors in econometrics is worth a careful reading:

Spurious regression, or nonsense correlationas they were originally called, have a long history in statistics, dating back at least to Yule (1926).Textbooks and the literature of statistics and econometrics abound with interesting examples, many of them quite humorous. One is the high correlation between the number of ordained ministers and the rate of alcoholism in Britain in the nineteenth century. Another is that of Yule (1926), reporting a correlation of 0.95 between the proportion of Church of England marriages to all marriages and the mortality rate of the period 1866-1911. Yet another is the econometric example of alchemy reported by Henry(1980) between the price level and cumulative rainfall in the UK. The latter relation proved resilient to many econometric diagnostic test and was humorously advanced by its author as a new theory of inflation. With so many well known examples like these, the pitfalls of regression and correlation studies are now common knowledge even to nonspecialists. The situation is especially difficult in cases where the data are trending- as indeed they are in the examples above- because third factors that drive the trends come into play in the behavior of the regression, although these factors may not be at all evident in the data. Phillips (1998).

Sure, it’s irrelevant and unresponsive, but, strictly speaking, it’s not entirely wrong.

I’ve read most all of the responses now (not very hard since they’re quite short.) Your remark above about irrelevant and unresponsive is a good summary of all of them. Actually I was tempted to post something even snarkier, but I think I’ll leave it to Steve (or Willis when he’s back and up to speed) if they desire. Let’s just say that it was quite obvious that there is no attempt to actually address the questions put before Dr. Junkes. BTW, I wonder if Dr. Junkes himself actually composed the responses. When he was here he was fairly responsive, if a bit pompous. I wonder if there was a mini-IPCC meeting to make sure that this summary for policy-makers will match the individual positions to be given out later.

]]>trying to make a distinction between

spurious regressionandspurious correlation?

That’s how I read it. Sure, it’s irrelevant and unresponsive, but, strictly speaking, it’s not *entirely* wrong. 😉

I agree that the DW test is “usually” used to test for autocorrelation of residuals, but the interest in autocorrelated residuals was prompted in part by Granger and Newbold 1974, Spurious Regression in Econometrics – linked to a url above – in which the DW test was suggested as a test for spurious regression.

If Juckes is trying to say that the test would apply to a regression, but not to a correlation, then you have to reflect on the underlying geometry. The correlation coefficient is the angle between the vectors in N-space. The regression coefficient between two normalized vectors is equal to the correlation coefficient. Any apparatus from one applies to the other.

Also, as noted in a post above, the variance-matching procedure of CVM is mathematically equivalent to a constrained regression in which the norm of the estimator is equal to the norm of the target. This is very simple mathematics, which does not cease to apply, merely because Juckes ignores it.

]]>I’m not aware of a standard test for spurious correlation.

I suppose there’s a technical definition of spurious correlation which would allow a test, but basically the concept shouldn’t allow a test. I.e. if something passes the tests for correlation but can’t have a true correlation for logical reasons, then it must be a spurious correlation.

I think usually when we have what is called spurious correlation we assume that it will disappear when later data comes in. This would imply that you could divide up the available data and look to see if the correlation disappears when hidden data is examined. Except that that would require no cherry-picking. If the data is cherry-picked all you can do is wait for new data.

]]>I’m not aware of a standard test for spurious correlation.

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