I’ve found an unlikely ally in my questioning of the smoothing of MBH99 in the original publication and in IPCC TAR: Keith Briffa.
Not that Briffa has posted a comment endorsing my observation. However, the smoothed version of MBH99 in Briffa et al 2001 (near contemporary with TAR) is virtually identical to what I got.
A CA reader has sent me a digitization of the MBH99 smooth and I’ve attempted to reverse-engineer the weights in the filter to yield the reported smooth. Even with reverse-engineering I’m unable to replicate the Swindlesque S-curve in the Mannian 20th century smooth (by “Swindlesque” here, I mean a curve showing a noticeable mid-century decline).
Reviewing the bidding, here is the graphic from IPCC TAR – we’re only discussing the MBH99 smooth for now.
Figure 2-21 from IPCC TAR.
I reported that I had been unable to replicate the upside-down S in the MBH smooth version (in IPCC here) and also in MBH99 and Mann et al 2000. Here’s my replication using a 40-year Hamming filter with end-period mean padding (as stated in the IPCC caption) as compared to the digitized version of the MBH99 smooth from the original article (this is zero-ed on 1902-1980 rather than 1961-1990 so the vertical scale is a little different, but that doesn’t affect the comparison below). The 40-year Hamming filter applied to MBH99 data (red) does not produce the Swindlesque S-curve in the 20th century that is in the MBH99 and IPCC smooth (black).
It turns out that I’m not the first person to have failed to replicate Mann’s closing slalom course. Here is an excerpt of the 1400-2000 period from Plate 3 of Briffa et al 2001, summarized online here with large graphic version here . The MBH99 smooth is in purple here and precisely matches the smooth that I obtained – without the Swindlesque S-curve of the MBH99 smooth in the 20th century.
I attempted to reverse engineer the weights in the filter by making a linear regression of the smoothed series against the original data with plus/minus K leads and lags, experimenting with different values of K between 15 and 30, all without success. Here is the fitted value using the stated bandwidth of 40 years.
For comparison, here are the reverse engineered filter weights compared against 50-year Gaussian weights and 40-year Hamming weights. Hamming weights have considerably longer tails than gaussian weights. The Mannian weights – which remain unknown if they even exist – have a considerable amount in common with Hamming weights, but do not match exactly. The implementation of Hamming weights used here is adopted from Meko’s lecture notes (Meko being a dendro and is a useful source of anthropological information on the statistical customs of dendros) and reconciles to Meko’s example.