Almost all lines drawn across time series to indicate trends are fake, frauds, misleading, or are improper ascriptions of cause.
Video
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HOMEWORK: Find your own time series with trendy trend lines. See if they suffer from the Deadly Sin of reification.
Lecture
Review the last Class: That’s Not Noise, That’s Signal! In it we learned that drawing straight lines, usually via regression, on accidental (and not per se) time series, like those in economics, the environment, sociology, and so forth, was wrong most of the time.
These lines assume there is a constant linear force, a cause, that is operating, something that is causing a signal, to which “noise” is added. This is false in most cases. Not all. Or not true in any large sense. There are sometimes direct linear causes. It’s possible. But you cannot prove the cause is there because you can draw the line. Any two points make a damned line. That does not mean that the same constant linear forcing caused both points.
Almost always the line is put on time series plots to hint, infer, or outright claim the linear causes exists. This is always wrong: it is backward. It is a fallacy. If the forcing really does exist, then we can draw a line. But since we can always draw a line, the act of drawing is no real indication the cause exists.
Today I prove it to you again.
Our example uses official government data (hence, as we are told, flawless). I wanted temperature, also an official obsession, and from Michigan, the greatest state. One site had average temperatures for each year and month. Since I was a weather forecaster (yes) in the National Weather Service at Sault Ste Marie (“The Soo”), I used that (that NWS station has since migrated south).
Here is that data below, which starts in 1931 and goes through July 2025. We today accept this data as coming from On High, and do not criticize it in any way. Those critiques will come another day. Gist: often the data is not the data.
Here’s the brutal truth about almost all accidental time series: the start and end date are themselves accidents. There is thus no good reason, other than convenience, to use these accidents as if they somehow had great importance.
Understand carefully. This example which follows applies to nearly every (accidental) time series you’ve ever seen. Yes, even your own. There is nothing special about weather data.
You are in 1955 and have just experienced a hot July, average of nearly 72 degrees (in civilized units). This worries many. Is this the start of an end-of-the-world heat wave? Are we all going to die? How can we Save The Planet! So you run a trend on all the data you have, from 1931 to 1955. That’s the first blue line.
It’s statistically significant! This proves, in those addicted to wee Ps, that the temperature is trending down. You have proven it! The P is wee! The line is down! The 72 is just noise.
You retire, calm and happy. The world will not end in heat, but in ICE.
Your successor thought you were crazy. There is no ICE death. There is only heat. So he decides to toss out your data, which is suspect, and to run a trend from your retirement to 1982.
Aha! A statistically significant increase! The world will be doomed by FIRE!
And then his successor in 2010 proves its ICE, then five years later it’s FIRE (my enemies turned the line blue which should be red).
You can go on and on like this as long as you have data. Lines can always be drawn.
The last two are to show the effects of just one tiny change in start date. The trends are both up, and “significant”, but the one that starts a year early shows a much larger upward trend.
Meaning if you wanted to sell your message, be creative in your starting or ending point. It’s easy. Just start the data from whatever point works best for your message. Almost no one will question what came before.
The difference in those last two red lines is big, in a relative sense. Remember all those headlines that claim “Hottest July Evah” or “Among the Hottest Evah”? The differences they are claiming are down to the tenth, sometimes hundredths, of a degree. This is ridiculous. But you can see how easy it is to say whatever you like. The more dramatic red line is 0.11 F a year, whereas the second, starting a year later, is 0.07 F increase a year. That’s huge in the terms those who fret over “climate change” use.
And we got it by being clever with our starting point.
Here’s a reminder where this was done in Real Life. I mean, where people go hunting for “change points” to “prove” their causes.
Again remember! This criticism applies to all time series, not just temperature or environmental data. Look for it everywhere.
Some of you will have thought the first example might not have been realistic. It was, but let’s take that question seriously.
Let’s suppose we are now in 1936. Now look at this picture.
In 1936 the NWS had 5 years of data. Plenty to do a trend. So they did. That’s the first dotted red line. Red for HEAT death. Dotted because it wasn’t “statistically significant” (a term which is as undead and destructive as any vampire). In 1937 we have one more year of data. So a new trend. That’s the second dotted line. Also HEAT, but no “significance.”
And so on for each year we get new data. This doesn’t seem like we’re cheating, since we are using the only starting point we have, and using all the data we have. That’s science!
By 1950, the trend is ICE—a new ice age. And “significant”! Now we’re worried, just like scientists were back then, though only becoming vocal, and well funded, in the 1970s. In 1951, still an ICE significant trend. So too in 1952, 1953, and so on.
After 1970, the “significance” is not there, but the ICE death signal is still there. There must be a reason for this cause, we reason. The lines are there, they must be real. It must be man that is causing the cause.
The Deadly Sin of Reification has you in its grip.
You call for a new ICE age. Crops will fail, millions, even billions will die. That happened. Not the crops or deaths, but the calls. (People with short memories now say these calls never happened. But we saved the documents.)
Finally, around 2011, the ICE has turned to HEAT, but not “significantly”. It has stayed on HEAT since then.
There must be a reason for this cause. The lines are there, they must be real. We must be in global warming, a.k.a. “climate change”. Crops will fail, millions, even billions will die.
That happened, too. Those calls. And are happening.
Some thing or things caused every point. The job of science is to find these causes. Cheap and reflexive tricks like drawing trend lines on time series can help. But they more often hurt.
Again remember! This criticism applies to all time series, not just in “climate change.”
HOMEWORK: Here’s the same picture, this time using different starting dates. The first is 2021 to 2025, the next is 2020 to 2025, and so on. Your homework is to critique this picture, and contrast it with the previous, which used different ending dates. The colors and linetype have the same meanings.
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