Monthly Archives: April 2014

Non-Linear Trends

Any given time series, say July average temperature in the Moscow region since 1881, might exhibit both short-term (more brief) and long-term (more lasting) patterns of change. The longer-term is certainly something worth knowing about. It might be increasing, or decreasing, or it might not be changing at all. It might have wiggled around a lot but not really gone anywhere until some new factor came into play. But whatever its pattern, we usually identify the longer-term pattern of change with the trend.

What we’re really after is the background level against which temperature variations have their sway. By “trend value” I mean exactly that: the background level at a given moment. If it changes while the nature of the fluctuations remains the same, the probability of record-setting extremes will of course change. When the background level is colder we’re more likely to get cold extremes, and when it’s hotter we’ll get more extreme heat. Pretty simple.

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