I'm having trouble figuring out whether its important to have a common period of time when performing hypothesis testing for trend analysis. I have time-series data of varied length - some sites have 5 years of data while others have 20 or even 40 years of record. If I filter my data based on a common time period then I exclude a large part of my data set. I can understand that comparing the magnitude of trends isn't valid but does it matter when simply testing for monotonic change?
If you are not interested in making any cross-site comparison of magnitude of trends or in computing an overall trend across all sites, then you don't really need to have a common time record across sites. However, if you have many sites, you may still want to group sites according to whether they have (approximately) common support for reporting purposes. Then you can present trends together for all sites where the time record spans a common period like, say, 2001-2005 (5 years worth of data), 2001-2010 (10 years worth of data), etc. This would make it easier for people to digest your results than if you report trends for ungrouped sites. In particular, if you choose a time span like 2001-2010 for your 10-year time series, you can group together trends which cover incomplete time records such as 2003-2009, 2002-2008, etc., by allowing a small fraction of data missingness in the incomplete time series relative to the complete record 2001-2010.
Thanks Isabella, its been very difficult finding information about comparing trends with different time periods. What you can and should not do. I really wanted to use the entire data set for all data ranges because collectively I think they highlight some interesting patterns - namely, we detect a far greater number of trends using summer months compared with other seasons. Related or not, this corresponds with peak groundwater abstraction, and our records show groundwater use has "significantly increased over time, particularly over the summer seasons.
We have two main groundwater basins in our region and I expect one is experiencing greater declines than the other. Here, I will look to use the same time period for comparing the magnitude of trends. Unfortunately, it seems to take quite some time before we detect statistically significant trends so my comparison might be limited to a 'small' number of wells.