Steve — IMHO, Newey-West greatly undercompensates for serial correlation, particularly when the dependent variable has been moving averaged, eg with a 5-year MA as here. Fitting an AR(p) to the residuals and using it to compute the autocovariance matrix is a big improvement, though even that still understates the adjustment, even if the errors themselves are AR(p) — the residuals will show less s.c. than the errors, and even if we saw the errors, OLS estimates of AR are biased in finite samples away from persistence.

Even if the original errors were serially uncorrelated, after taking a 5-year MA, only every 5th observation will be serially uncorrelated. This means that you would have to consider only every 5th observation in order for OLS se’s to be correct, but it’s roughly what has to be be done to undo the effect of the averaging.

If you really want to estimate a time-averaged relationship, a more efficient way to do it than throwing out 4/5 or whatever of the observations would be to simply regress the unaveraged dependent variable on the averaged independent variable. This will not introduce s.c. into the regression residuals, and will let you use the entire sample.

]]>Hansen and Lebedeff go from 1880 on; but CRU was available back to 1854. You can’t assume that they didn’t look at both.

Actually, what I was originally interested in testing here was the impact of the smoothing in the calculation, rather than the impact of the truncation – which is just as interesting.

For the unsmoothed data 1851-1985, the r is 0.19; it increases to 0.20 for 1895-1985. The OLS t-statistic is 2.3 and with Newey-West standard errors, it’s about the same.

Smoothing obviously changes hte autocorrelation properties and the effective degrees of freedom. For the smoothed data, the r increases to 0.39 from 1851-1985 (0.48 from 1895-1985). The OLS t-statistic is 4.94. However, with Newey-West standard errors, which is much more realistic with smoothed data, the t-statistic is only 1.15.

Smoothing to achieve “significant” correlations without allowing for the effect of the smoothing on standard errors is a very common Hockey Team statistical practice. Jones et al [1998] has a whole table full of “decadal correlations”.

]]>Is it possible that Hansen & Lebedeff used 1895 as a starting point, and Thompson carried it over? That would be careless rather than cherry-picking.p

]]>The “amount effect” is now distinguished from the temperature effect by many specialists and at least a sizeable minority do not appear to believe that dO18 is a temperature proxy in tropical glaciers. I haven’t seen this caveat expressed by IPCC however.

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