I have annual temperature data from a variety of weather stations in the Caribbean and I want to be able to show statistically that the trends for each station are significant, either positive or negative or no trend.
I can obviosly plot the data and fit a line, but I want to make a stronger argument than just eyeballing it. I was thinking about a runs's test or a Mann-Kendall test. Most everything I've read talks about ARIMA models, concernes about autocorrelation, etc. but I feel like those are for econometric predictions. I'm not trying to predict anything. I just want to be able show whether or not the increase or decrease in temperature is due to random chance, or not. (my n=49) I may have larger n values for other stations, but for right now, working with 1 station, I have 49 observations. It would be nice to be give some idea of how far above or below random chance it is.
I don't know this helps, but I actually have monthly data, but to avoid periodicity issues I've so far been playing around with July values to represent N. Hemisphere summers.
In terms of hypothesis testing, if the Caribbean is not warming, then none of the weather stations would show increasing trends in temperature.