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 […]

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 […]

Chas. has sent in a recipe for showing random walks in Excel. These sorts of things are much, much easier in R (see http://www.r-project.org for free download). I’ve posted up a little script below which generates random walks and ARMA(1,1) walks together with trend lines and t-statistics.

I’ve been posting up on some fundamental articles on spurious regression, involving autocorrelated processes. Here are some illustrations of what different examples look like, with specific comment on a realclimate article.

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 […]

The reason for looking at the form of stochastic process that bests suits the gridcell (and hemispheric) temperatures is that the statistical behavior of a random walk (one type of stochastic process) is very different than independent draw from a normal process.

I find it difficult to believe that so many scientists have seemingly accepted the realclimate argument that Preisendorfer’s Rule N applied to a principal components calculation is somehow a substitute for proper statistical analysis. To show the goofiness of this argument, I asked a friend to compile a list of weekly closing prices for 20 […]