Here are plots of the autocorrelation functions and time series for the 17 gridcells with the highest AR1 coefficients in an ARMA (1,1) model. The locations and patterns are a little curious.
First, I’ll illustrate the autocorrelation functions for a couple of NH sites with lengthy records. Here is 52.%N, 2.5 E (containing London) with a rather low AR1 coefficient.
Next, here is gridcell 42.N, 77.5W (containing Toronto) and New York state. There is relatively low autocorrelation and little trend.
Now for the sites with very high autocorrelation. I calculated autocorrelation for sites with at least 100 measurements. This has led to the inclusion of pretty sparse Southern Ocean sites. I’ve left them in, not because the autocorrelation is very realistic, but because they illustrate the sparseness of Southern Ocean records and issues about non-homogeneity. Here are the 15 sites with highest AR1 coefficients in an ARMA (1,1) model.
1. 7.5 S, 132.5 W. This is in the middle of the Pacific Ocean. The AR1 coefficient has 5 9s with a high -0.60 MA coefficient. Nineteenth century values are sparse. This combination of very high AR1 and medium negative MA1 coefficients is typical of tropical oceans – I don’t know why the value for this site is so high.
2. 57N, 62E. This is near Salekhard in Russia (in the same general region as the Polar Urals.) This combination of AR1 and MA1 is similar to what Deng  had in mind for "almost white near integrated" noise. The "sinusoid" form in the autocorrelation is quite common in CRU data (many other gridcells are stronger) and suggests to me that the normalization has not been performed very accurately. It also looks like the UHI in Salkhard may not have been adjusted correctly.
3. 57.5 S, 97.5 E. This is a Southern Ocean location near Antarctica south of Thailand. Data is very sparse and not much weight can be placed on the values. One wonders at how homogeneity was supposedly obtained.
4. 57.5 S, 52.5E. This is another Southern Ocean site near Antarctica, this time south of Oman (but a huge distance). Data is so sparse as to be almost meaningless. Again one wonders how homogeneity of this record was supposedly obtained and the benefit of such records in the data set.
5. 47.5 S, 52.5 W. This looks like ocean just to the east of the Falkland Islands. It looks like the gridcell must have somehow included information from the Falkland Islands, simply because the continuity of record keeping is hard to explain otherwise. The 19th century information and 20th century information look non-homogeneous. Also it looks like there may be an UHI effect, which might be possible if Falklands information was included in this cell somehow. I would presume that the sporadic measurements in between periods might be occasional ocean measurements.
6. 57.5 S; 47.5 E. This is another Southern Ocean site right beside #4, near Antarctica, due south of Saudi Arabia (a huge distance). Measurements are sporadic and one wonders at how homogeneity was supposedly obtained.
7. 57.5 S; 112.5 E. Another Southern Ocean site near Antarctica, due south of the ocean off the west coast of Australia. Measurements are sporadic and one wonders at how homogeneity was supposedly obtained.
8. 57.5 S; 37.5 E. Another Southern Ocean site near Antarctica, due south of Mozambique. Again, measurements are sporadic and one wonders at how homogeneity was supposedly obtained.
9. 47.5 S; 117.5 E. Another Southern Ocean site not as far south as Antarctica, due south of the ocean off western Australia. I don’t see any islands in the area and one wonders at why the records are so bunched – maybe there were whaling records in the 19th century. The records don’t look homogeneous to me.
10. 2.5N; 12.5 E. I discussed this one already: this is in Congo (not Zaire) and is clearly an artefact of some bad data.
11. 67.5S; 22.5 E. Another Southern Ocean site, this time really near Antarctica, south of South Africa. Again very sporadic data and hard to see how homogeneity could be established.
12. 27.5S; 52.5 E. Here’s one with some data. This looks like the ocean gridcell to the south of Madagascar. The continuity certainly suggests the influence of land measurements, perhaps extrapolated from Madagascar or South Africa or both. One would like to spot-check UHI handling here.
13. 52.5S; 47.5 E. Another Southern Ocean site, more or less due south of Iran. Measurements are sporadic with some questionable isolated measurements.
14. 52.5S; 7.5 E. Southern Ocean near Antarctica, way south of Nigeria. Sporadic data with questionable homogeneity.
15. 32.5S; 57.5 E. Here’s one with some data amounting to an "almost white near integrated" series. This is an ocean gridcell to the south-east of Madagascar. The continuity certainly suggests the influence of land measurements, perhaps extrapolated from Madagascar or South Africa or both. It looks like a similar information base as #9. The length of the record is puzzling – maybe Capetown is being factored in, or maybe it’s on a sailing route.
16. 47.5S; 92.5 E. More Southern Ocean rather like #7. One wonders at the different generations of data.
17. 2.5N; 117.5 E. This is from around Indonesian Borneo.It looks like there was a discontinuity in the records around 1950 with a step in the record. "Rural" Indonesian sites, which many people have never heard of, now have populations of 350,000 to 3 million and UHI in these tropical cities seems to me to be an issue here.
18. 32.5N; 102.5 E. This is from China, perhaps around Chungking. One would want to see UHI homogeneity.
As a comparandum to #2 showing a potential normalization issue, here’s the information from gridcell 12.5N, 47.5E (around Somalia) which shows a distinct autocorrelaiton pattern, suggesting defective normalization in one or more months.