I'm wondering if it make sense, or simply your opinion about this: I have a dataset with a value, and a time variable. let's suppose that the time variable is month, like
time = c(1,2,3,4,5), and the
value = c(2,3,5,2,4).
In this case:
time = c(1,2,3,4,5) value = c(2,3,5,2,4)
In your opinion (if months increase more than 12 in the next years), is it correct and does it make sense to calculate the Pearson Correlation
cor(time,value)  0.3638034
between time and value to see if there is positive, negative or not correlation (in this case positive)?
I think that as a formula could works, but I do not know it's an error to force the month a qualitative ordinal variable, to months in number, a quantitative interval variable and use them to Correlation.
I've thought this because:
I have a big quantity of"moving" small time series (add one incoming month, remove first month) long 6 months. I need to see,for each of these time series, if the trend is growing or decreasing without an inferential point of view (think about the small time series as is, not a sample of a stocastic process, I suppose).
I've thoght that the Correlation could help to see if there is a linear relationship between time and values, but reading all those answer, it does not seems the best way.