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.