how to compare short-term trend with a long-term trend?

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Marco Sandoval 2019-8-6

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https://ww2.mathworks.cn/matlabcentral/answers/475101-how-to-compare-short-term-trend-with-a-long-term-trend

Hello,

Let's asume I have this annual temperature data from 1966 to 2018 from one region:

temp = [11.9, 11.7, 12.2 11.6 11.4 11.6 12.2 11.4 11.4 11.7 11.8 12.6 12.5 12.0 12.6 12.6 12.7 12.3 12.0 12.4 12.5 12.9 12.1 12.5 12.1 12.4 12.4 12.6 12.7 12.3 12.8 13.2 12.5 12.5 12.4 12.0 11.8 12.5 12.6 12.4 12.5 11.5 12.7 12.3 12.2 12.2 12.7 12.5 12.85 12.8 12.7 12.6 12.5].

This looks like

Where in blue is the data, black line is mean, dashed black line is mean+-std, in red is the long-term trend and I put a transparent green rectangle in the last 5 years (2013-2018) to show an opposite trend in the last 5 years (purple line). How can I be sure that this short-trend is significant compared to the long-trend? Is there a method to compare these two trends and that can tell me "ok, this change in the last five years is something..." ? I'm trying to replicate this paper: Zador et al., 2016. Ecosystem considerations in Alaska: the value of qualitative assessments. ICES Journal of Marine Science (2017), 74(1), 421–430. doi:10.1093/icesjms/fsw144

Best regards,

Marco