I recommend that CA readers visit UC’s blog for some interesting discussion. (BTW UC visited Toronto recently and we had a nice dinner.) UC posted the following interesting figure on Unthreaded as follows: BTW, got interesting result when I replaced Temperature PCs with solar in MBH98 algorithm. Similar RE values as in the original, and […]

One of the papers that has most informed my views on multiproxy studies (and I’ve mentioned it from time to time) is Ferson et al. [2003], Understanding Spurious Regressions in Financial Economics which I read a couple of years ago. "Spurious regression" here is a false relationship between series, frequently observed with highly autocorrelated series […]

Huybers’ second and more interesting (to me) issue pertains to the benchmarking of the RE statistic.I’m going to start in the middle of this issue. If I start with the history e.g. defining the RE statistic and showing its history (and I just tried), it’s hard to get to the punch line. So what I’m […]

What is the standard deviation (variance) of an autocorrelated series? Sounds like an easy question, but it isn’t. This issue turns out to affect the spurious regression problem, so I’m posting up a short note on the problem. These issues are well-known in econometrics, where they have led to “heteroskedastic-autocorrelation consistent” estimators. There’s an interesting […]

I will go approximately 50-50 for a while on posting statistical and non-statistical notes. Today’s another statistical note. It’s a bit technical, but some of the statistical findings from econometrics on autocorrelated series are highly applicable to climate and, while there is occasional citation of econometric literature in climate articles and occasional forays by econometricians […]

Granger and Newbold [1974] provided examples of spurious significance in a random walk context. This has been extended by various authors to a number of other persistent processes. Granger and Newbold suggested that the DW statistic could be used to test the autocorrelation in the residuals, giving a test that could be used in a […]

"Spurious significance" was a phrase used in the title of our GRL article. We regarded this as perhaps the most essential point of the article, but it seems to have gotten lost. This is the second of a planned series of notes on spurious significance, to give a sense of the statistical background. Granger and […]

I’ve had a number of requests to explain some statistical topics and tests of significance. I’d rather not get involved in an explanation of general statistical concepts, which are perfectly well covered in many other places. However, I am going to post some notes up on “spurious significance”, which, after all, was part of the […]