I am looking at ways to forecast monthly time series data over a larger geographic region. I have time series weather data (e.g., temperature, precipitation) from multiple stations, and the stations are at certain proximity to each other. In the data set, temperature has slightly increasing trend while precipitation does not.

I want to forecast monthly temperature and precipitation for next 10 years using prior year observations. I want to combine prior temperature relationship with precipitation to forecast precipitation, and vice versa, which I think basically involves multivariate time-series analysis. Using the mean forecasted/predicted values and the range (i.e., 95th lower and upper percentiles or Standard deviation), I want to introduce inter-annual variability in the weather patterns. While introducing inter-annual variability in the weather pattern in each stations, I want to preserve the existing spatial relation observed among stations. For example, if a station A has a temperature of 11 C, Station B should have similar temperature although not the same. Has anyone have any idea about the ways to handle this problem? I have been exploring approach such as ARIMA and ETS, but have not figure out quite well how to come up with better estimates. Any suggestions would be highly appreciated.

Also, I have been exploring the use of AMELIA in this case. Does anyone have opinion about the use of AMELIA as a forecasting approach? I know AMELIA is a imputation model but I don't know quite well if it has forecasting capability.

  • $\begingroup$ I'd say up front that forecasting monthly temperature and precipitation for the next 10 years is impossible. Not to totally discourage you, but no weather organization attempts anything like that as far as I know. $\endgroup$ – Wayne Apr 2 '13 at 19:31
  • $\begingroup$ I totally agree with you that weather organization has made no attempts forecasting weather for next 10 years and there are lots of uncertainties on this attempt. I was just wondering if it is possible to do this statistically. Capture the trend of the past and come up with forecast although the reliability of that forecast is questionable. $\endgroup$ – Sami khanal Apr 3 '13 at 16:12
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    $\begingroup$ Depends whether you're talking about climate or short term weather. There are lots of predictions flying around about average temperatures over the next couple of decades. It's not going to tell you whether to expect a rainy birthday in 2017. $\endgroup$ – conjectures May 21 '13 at 10:36

If the weather is a stationary process (debatable) then your long term prediction under some sort of ARIMA model (with seasonality) is likely going to be the process mean (with a large but bounded standard error). The interpretation of which is you should expect the average but anything might happen :) - useful!

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