Time Series Analysis Threshold Value

#1
I have time-series data for 0 min, 5 min, 10 min, etc. for 5000 genes. (Gene expression). I want to set a threshold value to eliminate reads that are just "noise," so that they do not contribute too much to the fold-increases/decreases that I am trying to analyze.
What is a good way to determine this threshold value? Is there a statistical test perhaps that I could run to determine this value?

Sample Data:

Gene Name 0 min 5 min 10 min 15 min 20 min
YFG 466 505 610 1530 1672
NJB 0 0 13 2 0
BNJ 325 1813 2257 3676 1757
JBN 3118 2953 2061 1159 1179
RNJ 977 1540 1248 908 801

Thanks in advance for your time!