Tag Archives: toeplitz

PCs in a Linear Network with Homogeneous Spatial Autocorrelation

Mar 24, 2008 – 1:13 PM

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 […]

By Stephen McIntyre | Posted in General | Also tagged , | Comments (12)

More on Toeplitz Matrices and Tree Ring Networks

Mar 23, 2008 – 8:50 AM

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 […]

By Stephen McIntyre | Posted in General | Also tagged , , | Comments (41)

Toeplitz Matrices and the Stahle Tree Ring Network

Mar 22, 2008 – 7:48 AM

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 […]

By Stephen McIntyre | Posted in Data, Multivariate, Proxies | Also tagged , | Comments (27)