Estimating the short-time rate of change in the trend of the Keeling curve.

What exactly is the short-time rate of change (growth rate) in the trend of [Formula: see text] data such as the Keeling curve? The answer to this question will obviously depend very much on the duration in time over which the trend has been defined, as well as the smoothing technique that has been used. As an estimate of the short-time rate of change we propose to employ a very simple and robust definition of the trend based on a centered 1-year sliding data window for averaging and a corresponding centered 1-year difference (2-year data window) to estimate its rate of change. In this paper, we show that this simple strategy applied to weekly data of the Keeling curve (1974-2020) gives an estimated rate of change which is perfectly consistent with a more sophisticated regression analysis technique based on Taylor and Fourier series expansions.