How would I work out if my data (sea ice extent) has a statistically significant trend (increase/decrease)? It is one value per year from 1979 to 2017.

  • $\begingroup$ There is no significance test without a model for time series and there are many such models. @IrishStat (answer below) is fond of the ARIMA family while many people are fond of quite different approaches, including regression in some function of year. (Scientific aside as some-one who has worked on such data: this isn't a research question for any area I've heard about. Trends are established.) $\endgroup$ – Nick Cox Mar 21 '18 at 14:45
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    $\begingroup$ Au contraire regression models are a proper subset of comprehensive time series analyses possibly leading to no ARIMA structure being needed. $\endgroup$ – IrishStat Mar 21 '18 at 14:54
  • $\begingroup$ stats.stackexchange.com/questions/18336/… is an example of this. $\endgroup$ – IrishStat Mar 21 '18 at 15:01
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    $\begingroup$ @IrishStat That's a little hard for me to decode even knowing something about your modelling preferences. Regression without regard to dependence structure in time may be in practice and in principle anything from ill advised to good enough for a researcher's purposes, but it can easily be done without any attention whatsoever to ARIMA ideas. It's my impression that most of the cutting-edge approaches to time series qua time series seem to have left ARIMA on one side, but comments back and forth won't establish that view or its contrary. $\endgroup$ – Nick Cox Mar 21 '18 at 15:04
  • $\begingroup$ For sure you can ignore potential arima structure and/or anomalies . I just try to reach for higher ground that the data knows about and the user should find out about.. $\endgroup$ – IrishStat Mar 21 '18 at 15:08

Simultaneously identify ARIMA structure and any deterministic effects such as pulses ,level shifts, local time trends, changes in parameters over time and changes in error variance over time. See deviation from the trend on seasonal data for a discussion and also see How to determine order of sarima?

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  • $\begingroup$ Question clearly specifies no data on seasonal variations. $\endgroup$ – Nick Cox Mar 21 '18 at 14:42
  • $\begingroup$ where does he say no data is available ? $\endgroup$ – IrishStat Mar 21 '18 at 14:43
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    $\begingroup$ "one value per year" ! $\endgroup$ – Nick Cox Mar 21 '18 at 14:46
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    $\begingroup$ while that is true ..it does not necessarily suggest that there is no latent seasonality that might be detectable say a 5 year cycle found via search procedures. plus the discussions that I referenced dealt with the need to approach arima structure and deterministic structure in a comprehensive way. $\endgroup$ – IrishStat Mar 21 '18 at 14:48
  • $\begingroup$ Absolutely: seasonality is very real and in fact for such data dominates trend. Researchers in this field do know this and -- evidently -- in this case the OP is asking about annual data because that may be all that are available for one area or seasonality is being ignored. $\endgroup$ – Nick Cox Mar 21 '18 at 14:54

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