I'm fairly new to statistics in general and R specifically and am taking a biophysics course which uses both. My project is to determine trends in temperature and precipitation for my region, using daily measurements from a single monitoring station. I have daily values for Ave. Temp, min, and max, as well as precipitation. From what I have found in my research it seems like ARIMA may be the most effective option available (RHtestV4, etc. don't seem to be available to the public). Would you recommend using ARIMA modeling or is there another option available?

I've tried linear regression but even going to yearly means, there is still too much variance to obtain a decent trend line. Any information or tips would be immensely appreciated.

Thank you.

  • $\begingroup$ Daily temperature can certainly be modeled as a time series given that you have daily measurements. Take the average temperature over time and fit an ARIMA model and see if it fits well. The same can be done with precipitation. There are other forms of time series model that can be fit such as ARCH and GARCH. Search the site and you will find lots of discussion about these models. $\endgroup$ – Michael R. Chernick Apr 20 '17 at 5:54
  • $\begingroup$ You will probably need to look into seasonality $\endgroup$ – kjetil b halvorsen Apr 20 '17 at 8:44
  • $\begingroup$ Another idea which I now is used with temperature data is Kalman filters:ecmwf.int/sites/default/files/elibrary/1996/… journals.ametsoc.org/doi/pdf/10.1175/… $\endgroup$ – kjetil b halvorsen Apr 20 '17 at 8:46

I think it can. Campbell & Diebold (2005) use an ARX-GARCHX model for point and density forecasting of daily average temperature in Atlanta, Chicago, Las Vegas, and Philadelphia.

They compare their forecasts with a few competitors, the best among which is the forecasts from Earth Satellite (EarthSat) corporation which are used to settle temperature-related weather derivative products traded on the CME. In the end, ARX-GARCHX never beats EarthStat, but still looks quite well considering that the model is rather simple (conceptually -- and especially computationally) as compared to models used by professional weather forecasters.

Point forecasts: ARX-GARCHX does worse than EarthSat forecasts in 1-4 day horizons, but already in 5-8 day horizons the difference in forecast accuracy between the methods is not statistically significant. Beyond 8 days, ARX-GARCH does roughly as well as the EarthSat forecast.

Density forecasts: No comparison between EarthSat and ARX-GARCH (?).



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