I once wrote an X-ray diffraction data analysis program that had a user-controllable variable averaging window size with user-adjustable weighting for each observation within a window. It used some new statistics I “invented”, like the mean deviation from the mean, the median deviation from the mean, the mean deviation from the median, and the median deviation from the median. The crystallographer I was working for loved fiddling with these buttons.

You could do stuff like that with Fortran.

For a time series, such as the stock market, sea ice extent, or the output of a photovoltaic system, moving averages are very useful for spotting trends. Adjusting the period of the moving average can show long and short-term patterns. Taking the last example – a PV system – will see a wide range of daily harvest amounts. Cloudy days at any time of year will result in only a few kilowatt hours. A sunny day in winter might produce only half as many kWh’s as a sunny day in summer. By generating a 30 day moving average, one can predict what the same period next year should average. By using a 90 day moving average, seasonal norms can be visualized. Comparing yearly moving averages can show how the system is doing over its lifetime. For sea ice and glacial data, a five year moving average would be useful for assessing the over-all gain or loss of the system.