I'm a geographic student and I'm studying time series of vegetation index. I'm french and even if I'm quite fluent in communicating in english, I may lack some specific vocabulary needed to be precise in what I'm asking, please forgive me for that.

I have a scene with 374 dates, and for each pixel I extract some tendancy which are linear. For each of these lines I've got a slope value, and for each pixel I can have from 1 to generally 5 slope values.

If the slope is positive, then I can consider a greening tendency of the area for the period, and if it is negative, it means some browning tendency. The point is I have some slope values that are near 0, and some extrem others that are around +/-140. So I cannot consider the period near zero really as a greening/browning period.

My question is as follow : is there a statistical method which could help me figure out what threshold to use to consider the slope as 0 (nor greening nor browning), like between +/-0.01 or +/-0.1 or +/-1...?

Obviously, since I am wrinting a research paper, I do not ask for some threshold values, but more for some direction were to look to find it myself, I cannot even figure out what to google to get this information...

hi,
I don't think I understand your problem completely but at the first sight this is pretty much what the significance test would tell you. Slopes that are not significant might be just a random fluke, significant slopes probably not. The best part is that you do not need a threshold, the calculation will take random fluctuations into account.

Thank you for answering me. I am not very familiar with statistics, so, despite what I said that I could do with just some direction, I've got two other things I'd like to ask:

- first I'll try to be a bit more clear on what I'm trying to do. Have some few hundreds thousands of pixels and for each of them there is one or more linear tendency with their own slope coefficients. If the range of the coefficients would have been betwenn +/- 2, I guess I couldn't decently consider as null coefficients ranging between +/-0.1, while if, like here, the range is +/-140 (although it seems these are extrems that happen more as exceptions), and most coefficients are around +/-25, a coefficient around 0.5 could maybe be considered as not significant. And since I'm no good to figure out the best threshold for my distribution, I'm looking for a statistical method to do so. I hope this is more clear...

- what kind of test are you talking about ? A google search led me to the Student test, but even if I found it under "significant test of a coefficient", I'm not sure it can answer my needs. If these are more clear, what do you think ?

hi Girish,
when you were speaking of a trend I assumed that that is the result of a regression. E.g. something like you have 5 pictures, say, in a time order p1, p2...p5. You take a specific pixel and measure the value on each picture to get v1, v2...v5. With these 5 values you can build a regression model v=a0+a1*t and then you can calculate the significance of the coefficient a1 (aka trend).

This is probably not reaistic for 100 000 pixels but maybe you can build groups (say blobs of 10 pixels) and calculate the average value over the group and build the model?

I do indeed have trends resulting from some form of regression. And since what you are saying seems to make sense, I'm guessing I'm lacking the needed knowledge allowing me to fully understand what you means...

The case is as you present it (with 420 000 pixels, but I'm working with R, so number is not really a problem). And since it seems for you to obviously be some test of significance that I'm looking for, then I think I need to try harder and look deeper into it. Unfortunately, it always seemed to me that the terms used in statistics are tricky, so I'm not sure what to understand when it is referred as "significance", nor did I understand yet how this test works... But again it is on the account of my lack of basic knowledge in statistics.

Anyway, thank you very much for your answers, it allows me to look in the right direction, up to me now to figure out where I'm going.