The autocorrelation of the «blade» segment of «hockey - stick» shaped proxies is significantly higher than the rest of the series, this biases their
estimates of autocorrelation parameters because their model assumes a stationary autocorrelation structure, making their simulated series unrepresentative of most of the length of hockey - stick series, as can be seen in this graph of lag - 1 autocorrelation coefficients.
The other term is the variance of the estimation error in the regression parameters, and this varies in magnitude depending on the values of the proxies and also the
degree of autocorrelation in the errors.
In addition to the multicollinearity problem (for which explicit tests exist) and the simultaneity issue there is the ever present
question of autocorrelation of time series data.
Because of the autocorrelation in most geophysical time series, a validation period adjacent to the calibration period can not be truly independent; if the autocorrelation is short term, the lack of independence does not seriously bias the validation results.
Stationarity tests, the white noise test, and the Dickey - Fuller test for unit roots were performed as well as examination
of autocorrelation function and partial autocorrelation function plots17 to help identify appropriately parameterized models for MAR, ED, and lunch participation time series.
«(d) Having a slightly higher
magnitude of autocorrelation -LSB-...] does not turn a stationary simulation into a non-stationary simulation.»
The simplest, a chain of length one month («AR (1)» in the plot), doesn't do it, but one of just two months length («AR (2)») works pretty well (subtracting it from the sample noise moves
most of the autocorrelations into the zero uncertainty range).
To this aim we have screened our electrophysiological recordings of the magnocellular neurons, previously obtained from acute slices, with an
analysis of autocorrelation of action potentials to detect a rhythmic drive as we recently did for organotypic cultures.
I do not understand why there was no
discussion of autocorrelation, at least up to and including the OLS regression of one cumulative variable on another cumulative variable.
Then there's another broad
bump of autocorrelation at about 3 years, possibly reflecting the effect of ENSO (El Niño / La Niña).
The standard deviation of the OHU estimate as computed from the regression residuals is 0.031 W / m ², but because
of the autocorrelation implicit in using overlapping pentadal averages the true figure will be much higher.
And, in fact, McCulloch did not ask Nature for acknowledment for advising Steig et al of an error (i.e. the failure to take into account the
effect of autocorrelation on the significance of estimated trends).
We can compute them for each data series separately, and also compute uncertainty levels for those estimates (which are corrected for the
influence of autocorrelation, confidence intervals are 2 - sigma):
by removing the influence of exogenous factors like el Nino, volcanic eruptions, and solar variation (or at least, approximations of their influence) we can reduce the noise level in temperature time series (and reduce the level
of autocorrelation in the process).