I have the following time series:
df <- structure(c(288L, 259L, 265L, 293L, 271L, 278L, 300L, 286L, 278L, 275L, 282L, 285L, 290L, 296L, 296L, 279L, 270L, 292L, 283L, 289L, 280L, 269L, 289L, 290L, 287L, 271L, 280L, 299L, 278L, 287L, 293L, 286L, 297L, 281L, 285L, 305L, 288L, 295L, 277L, 292L, 286L, 281L, 287L, 302L, 292L, 297L, 292L, 279L, 281L, 291L), .Tsp = c(1961, 2010, 1), class = "ts")
I would like to know, which point in the time series is the start of a significant trend. Applying a Mann-Kendall trend test for the whole time series gives a significant trend. However,by visual inspection, the time series does not have an increasing trend at least over the fisrt half.
This is like a changepoint problem, but I am not sure, which detection method is appropriate for this. I just want to determine the point in the time series before the most significant increasing trend.
I am thinking of a moving Mann-Kendall trend test and plotting the corresponding tau statistic. But I dont know how to set a threshold value and test the significance of the tau statistics.
Any suggestions on how to do this correctly in R?
I'll appreciate any help.