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I have about 20 years of data, each year has a number of observations. If I put a linear trend through the data, I get a trend, and this trend differs based on the the choice of start and end year, which to some extent feels arbitrary. Is there an established method to estimate time trends for data like these where you might sample some years, estimate a trend, resample etc to come up with a distribution for the trend, and thus provide some confidence interval for the trend?

I see moving window regression might be an option, but what would guide the choice of window? And how would you integrate all the results to make some inference about the trend.

Bootstrapping might be an option. What would be a principled way to approach the sampling?

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    $\begingroup$ I'm confused why you would want to use bootstrap. From my understanding you have time series data so you should choose some ARIMA model or other time series approaches $\endgroup$
    – xcesc
    Commented Apr 15 at 5:39
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    $\begingroup$ I’m not looking to forecast the next few time points, which ARIMA would likely be good at. I’m looking to understand the general trend for the last two decades, and hence implications for the next two decades under ‘business as usual’. $\endgroup$
    – Mark Neal
    Commented Apr 15 at 19:05
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    $\begingroup$ I recommend mgcv::gam, it is veru flexible and has nice properties. fromthebottomoftheheap.net/tag/gam $\endgroup$
    – Simon Woodward
    Commented Apr 16 at 0:20
  • $\begingroup$ Flexibility and nice properties seem useful for fitting the existing data - does that help with identification of the long term trend? $\endgroup$
    – Mark Neal
    Commented Apr 16 at 2:13

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