## 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.