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Mar 3, 2010 9:32 AM
(5923 views)

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

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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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.

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

Regards,

Randy

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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,

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

Thanks,

Highlighted
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.

- Mark as New
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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.