A post just to let you know that laypeople appreciated the paper also. I would like to see a comment or two from Hu M on the author’s calculations and methods.

]]>Good find Ross. It’ll be interesting to see how, if at all, the IPCC handles this contribution in AR5. ]]>

Beran [11]

is a good reference, linear trend is fitted to Jones monthly NH 1854-1989 temperatures, 95 % confidence interval for time trend [-0.000158 ... 0.000802] if long memory is taken into account.

But AR4 Table 3.2. says that

The Durbin Watson D-statistic (not shown) for the residuals, after allowing for first-order serial correlation, never indicates significant positive serial correlation.

so Beran must be wrong.

Somewhat relevant text I cited here :

The ACLRM is presumed to be ‘the’ appropriate model, even though the residual autocorrelation could have arisen in numerous alternative ways, one of which is that the error follows an AR(1) process.

ACLRM = Autocorrelation- Corrected Linear Regression Model

]]>Thanks for posting this. It is interesting, though not surprising, especially to those who’ve been paying attention to the LTP literature (Koutsoyiannis in particular).

]]>Interesting paper. They conclude (my bold):

With respect to the time trend coefficients, the values are positive though they are statistically insignificant, which is in contrast with the results based on I(0) disturbances. The fact that the time trend coefficients are found to be insignificant in our work does not necessarily rule out the hypothesis of warming in the temperatures since

this can be a consequence of the sample size usedor even misspecification of the model.

If someone has access to the IMPROVE-series, I think it might be worth repeating the experiment with that dataset.

]]>Persistence and Time Trends in the Temperatures in Spain

Luis A. Gil-Alana

Abstract:

This paper deals with the analysis of the temperatures in several locations in Spain during the last 50 years. We focus on the degree of persistence of the series, measured through a fractional differencing parameter. This is crucial to properly estimate the parameters of the time trend coefficients in order to determine the degree of warming in the area. The results indicate that all series are fractionally integrated with orders of integration ranging between 0 and 0.5. Moreover, the time trend coefficients are all positive though they are statistically insignificant, which is in contrast with the results based on nonfractional integration.

So persistence matters after all when deciding whether a trend is significant. The IPCC’s treatment of this issue was a real scam. Remember that after the 2nd review round they had inserted the following paragraph based on reviewer comments (who were drawing from peer-reviewed literature) to which the lead authors had no response except hand-waving and denial:

Determining the statistical significance of a trend line in geophysical data is difficult, and many oversimplified techniques will tend to overstate the significance. Zheng and Basher (1999), Cohn and Lins (2005) and others have used time series methods to show that failure to properly treat the pervasive forms of long-term persistence and autocorrelation in trend residuals can make erroneous detection of trends a typical outcome in climatic data analysis.

Then with no authorization this paragraph was subsequently deleted from the published IPCC report. They can remove the text about persistence from the IPCC report, but they can’t remove the persistence from temperature data.

]]>What was stumping me was how to write out a recursive one-pass formula for the likelihood. Evidently there just isnt one!

Hosking [1984] presents a remarkably accurate approximation to the FARIMA (*arfima*) likelihood function that avoids using the full correlation matrix. Although this amounts to just a numerical shortcut — the Cholesky-decomposition approach will work — it is of practical importance: Long-term persistence may require keeping track of thousands to millions of lagged correlations, and the corresponding correlation matrix thus may have millions to trillions of elements.

Hosking, J. (1984), Modeling persistence in hydrological time series using

fractional differencing, Water Resour. Res., 20(12), 1898 1908.

I used SOM 3220 data from NCDC, which is relatively unadjusted. (Areally at most). This is not a USHCN site, and so doesn’t get the full battery of CDIAC adjustments. In any event, it has always measured at midnight, so there is no TOB to worry about, and apparently has always used glass thermometers so there is no MMTS adjustment to make.

Wooster OH, which is also in CRU and is relatively unurbanized, shows a distinct downtrend since 1920 or 1930 in the 3220 data. I haven’t tried to test it for any kind of significance yet, though, as I’m still trying to figure out how to get data through 2006 with and without all the adjustments. (It switched from midnight to 0700 and then 0800, which is a relatively small TOB, but I might as well use the official adjustments for this.)

I’m guessing that the downtrend for Wooster will also be insignificant, but that the difference between the two stations since 1948 will have a significant trend, indicating progressive urbanization of the Columbus airport site, and therefore the unsuitability of it and stations like it for CRU.

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