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## Statistical Significance on Time Series Trend

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?

Thanks!
-Chris
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Community Trekker

## Re: Statistical Significance on Time Series Trend

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.
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## Re: Statistical Significance on Time Series Trend

Hi Chris, Well if you have SAS/ETS you can use Proc UCM to perform your time series trend and it does output a p-value of various trends, cycles, level shifts, and irregularities.

Regards,
Randy
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Community Trekker

## Re: Statistical Significance on Time Series Trend

Randy,
Unfortunately I don't have SAS, I use JMP. What does the SAS proc include? Is there an analogue in the JMP software?

Thanks,
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Community Trekker

## Re: Statistical Significance on Time Series Trend

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.