Tag Archives: toeplitz

PCs in a Linear Network with Homogeneous Spatial Autocorrelation

As I observed a couple of posts ago, the Stahle SWM network can be arranged so that its correlation matrix is closely approximated by a Toeplitz matrix i.e. there is a “natural” linear order. I also noted that results from matrix algebra proving that, under relevant conditions, all the coefficients in the PC1 were of […]

More on Toeplitz Matrices and Tree Ring Networks

Yesterday’s results connecting eigenvector patterns in the Stahle SWM network to Toeplitz matrices and spatial autocorrelation were obviously pretty interesting. Needless to say, I was interested to test these ideas on out some other networks and see how they held up. There is a large literature on spatial autocorrelation and there appear to be well-known […]

Toeplitz Matrices and the Stahle Tree Ring Network

One of the most ridiculous aspects and most misleading aspects of MBH (and efforts to rehabilitate it) is the assumption that principal components applied to geographically heterogeneous networks necessarily yield time series of climatic interest. Preisendorfer (and others) state explicitly that principal components should be used as an exploratory method – and disavowed any notion […]