# How to detect an increase in a loess model fitted value at the end

Sorry if the question is trivial, but I'm not finding a proper idea for this issue.

I'd like to find if a series of fitted value of a loess is increasing in the end.

I'm working with some data like this:

data(economics, package="ggplot2")
economics$index <- 1:nrow(economics) economics <- economics[1:45, ]  And I am fitting a loess model to them, using the base R function: model_1 <- loess(uempmed ~ index, data=economics, span=0.40)  With this result for the fitted values: plot(model_1$fitted, type ="line")


Is there a way to detect the last high increase of the fitted value? I'm posting here because I am probably missing the point of something in the theory, rather than in the coding.

The only things I can think are arbitrary ways, like a condition if the last value is x times bigger than the mean of the fitted values without it, so there is an increase, or maybe a kind of comparison of the mean of the last n values vs the mean of the previous m values, but they seems too much subjective.

Thanks in advance.

• stats.stackexchange.com/a/225504/11849 Dec 5, 2018 at 9:06
• @Roland , thanks for the comment. Are you suggesting to calculate a global maximum? If so, how can I decide if it's in the end? Sorry I think that could be a nice hint but I'm not grabbing how to use it.
– s__
Dec 5, 2018 at 12:56
• The curve might go up or down at the end, so here is what I would try: find the peak-to-peak value of my data, and if the difference between a (smoother) quadratic and the loess is outside plus-or-minus half of the data peak-to-peak then I should have found this condition. Dec 5, 2018 at 16:31