I am looking for a way to assess the statistical significance of a trend in a time series data set.
For instance the "Seriesg" example data set in JMP (the airline passengers set) shows a steady increase in the "log Passengers" variable. It has a cyclic pattern and the "JMP Start Statistics" book discusses this on pg 531.
But what I cannot find anywhere is a way to get a t-test on the slope of the trend.
It is clear this trend isn't hard to see, but if I have noisier data and I'd like to get a t-test on the slope of a linear regression on the trend that isn't biased due to autocorrelation, how do I do that?
You can use "time" as your linear trend input. In the JMP time series module, select "log passenger" as y, and time as both a time id and as an input. You'll want to fit this as a Transfer Function.
I got best results using an autoregressive order 3 and a seasonal autoregressive order 1, with time checked as a simple input. The residuals are not autocorrelated, and slope is siginficant t < 0.0001.