Lines, Sines, and Curve Fitting 6 – backcast and forecast
This is a long post, so I am going to place it behind the “fold.” Click on the read more link to see the curve fits from the previous posts backcast and forecast. This might be a good post to practice your browser’s zoom features.
Line with Sine on Residuals
R2[1900-2000]= 0.89
R2[1880-2000]= 0.90
R2[1880-2010]= 0.91
Sine with Line on Residuals
R2[1900-2000]= 0.86
R2[1880-2000]= 0.85
R2[1880-2010]= 0.81
Sine with Sine on Residuals
R2[1900-2000]= 0.86
R2[1880-2000]= 0.64
R2[1880-2010]= 0.55
Line and Sine Simultaneous
R2[1900-2000]= 0.89
R2[1880-2000]= 0.90
R2[1880-2010]= 0.91
Sine and Sine Simultaneous
R2[1900-2000]= 0.89
R2[1880-2000]= 0.80
R2[1880-2010]= 0.86
Exponential with Sine on Residuals
R2[1900-2000]= 0.89
R2[1880-2000]= 0.90
R2[1880-2010]= 0.92
Sine with Exponential on Residuals
R2[1900-2000]= 0.86
R2[1880-2000]= 0.84
R2[1880-2010]= 0.81
Exponential and Sine Simultaneous
R2[1900-2000]= 0.89
R2[1880-2000]= 0.90
R2[1880-2010]= 0.92
We have some obvious “winners”:
[89,90,92] Exponential and Sine Simultaneous
[89,90,92] Exponential with Sine on Residuals
[89,90,91] Line and Sine Simultaneous
[89,90,91] Line with Sine on Residuals
And some obvious “losers”:
[86,64,55] Sine with Sine on Residuals
[86,84,81] Sine with Exp on Residuals
[86,85,81] Sine with Line on Residuals
[89,80,86] Sine and Sine Simultaneous
The lesson here seems to be “Don’t try to include a sine function in models of recent temperature trends.” Am I right?
You can get what looks like a good fit … if you use all the available data and don’t do any outside-of-sample testing. Your exp + sine model looked good for the 20th century, but underpredicted the past decade’s temperatures. The other ones are even worse.
One can make a nice-looking exp + sine model using all the data 1880-2010. Will it still look good in 2020? Who knows?
Perhaps somebody should run this on the internet:
1,$s/climate cycle/climate oscillation/
I don’t know, Ned. I think the lesson might be “things changed in the late60s/early70s.
There was a flat/cooling period of about 25-30 years from the early 40s to the late 60s-early 70s. Tisdale lately called it a climate shift. Tamino notes it as the beginning of something new.
Was the 25-30 year cooling natural? If so, why? If so, is it periodic? For me, those questions are still on the table.