The wiggly line in Figure (a) shows the global average surface temperature anomaly for the last 166 years. The solid line shows the so-called “trend” fitted by ordinary least squares regression of temperature on time. The dashed curve shows this trend plus a “multidecadal oscillation”.
Figure (b) shows the time series of residuals, i.e. what is left behind when the dashed line is subtracted from the original data.
Figure (c) shows the autocorrelation function of the residuals. These are all positive from Lag = 1 to Lag = 30 indicating that the residuals are highly self-correlated and that this simple linear regression model must be rejected at a high level of significance.
However an alternative, stochastic, “ARMA” model gives residuals which are not self-correlated and which does fit the data very well indeed. This model indicates that there are no significant trends and oscillations in the data.
The apparent trend is due to the false correlation which occurs when “red noise” data are regressed on time as the explanatory variable. This phenomenon is well known in Econometrics.
There is no rising trend in global average temperature. The observed variations are due entirely to red noise also known as a “centrally biased random walk”.
The paper has been accepted by Energy and Environment. A preprint can be downloaded here.