Home > GIStemp, LSCF > Lines, Sines, and Curve Fitting 6 – backcast and forecast

Lines, Sines, and Curve Fitting 6 – backcast and forecast

2011 January 14

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

line sine 1900 2000

R2[1900-2000]= 0.89
R2[1880-2000]= 0.90
R2[1880-2010]= 0.91

line sine 1880 2010


Sine with Line on Residuals

sine line 1900 2000

R2[1900-2000]= 0.86
R2[1880-2000]= 0.85
R2[1880-2010]= 0.81

sine line 1880 2010


Sine with Sine on Residuals

sine sine 1900 2000

R2[1900-2000]= 0.86
R2[1880-2000]= 0.64
R2[1880-2010]= 0.55

sine sine 1880 2010


Line and Sine Simultaneous

both line sine 1900 2000

R2[1900-2000]= 0.89
R2[1880-2000]= 0.90
R2[1880-2010]= 0.91

both line sine 1880 2010


Sine and Sine Simultaneous

both sine sine 1900 2000

R2[1900-2000]= 0.89
R2[1880-2000]= 0.80
R2[1880-2010]= 0.86

both sine sine 1880 2010


Exponential with Sine on Residuals

both sine exp 1900 2000

R2[1900-2000]= 0.89
R2[1880-2000]= 0.90
R2[1880-2010]= 0.92

both sine exp  1880 2010


Sine with Exponential on Residuals

both exp sine 1900 2000

R2[1900-2000]= 0.86
R2[1880-2000]= 0.84
R2[1880-2010]= 0.81

both exp sine 1880 2010


Exponential and Sine Simultaneous

both exp sine 1900 2000

R2[1900-2000]= 0.89
R2[1880-2000]= 0.90
R2[1880-2010]= 0.92

both exp sine 1880 2010


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

  1. Ned
    2011 January 14 at 5:43 am

    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/

  2. 2011 January 14 at 11:36 am

    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.

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