<Text-field style="Heading 1" layout="Heading 1">Code for the model</Text-field>

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Contest Program

JSFH

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC8lK2V4ZWN1dGFibGVHRj0vJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRidGOQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

HadCRUT (4.4.0.0), for years 1880-2014.

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print(); # input placeholder

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<Text-field style="Heading 1" layout="Heading 1">Code for the model</Text-field>

The time series were generated via a mixture model. Code for each of the three main submodels is below.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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

print(); # input placeholder

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 2" layout="Heading 2">ARMA code</Text-field>

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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<Text-field style="Heading 2" layout="Heading 2">fGn code</Text-field>

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

NiI=

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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<Text-field style="Heading 2" layout="Heading 2">Model 3 code</Text-field>

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print(); # input placeholder

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print(); # input placeholder

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The intuition here is that if the temperature shock has the same sign two years in a row, then

the climate system has effectively received a double shock, and then\342\200\224it seems reasonable to

hypothesize\342\200\224the system will react to that in some way. Tests show that this fits fairly well (see below).

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<Text-field style="Heading 1" layout="Heading 1">Parameter estimation</Text-field>

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<Text-field style="Heading 2" layout="Heading 2">ARMA parameters</Text-field>

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print(); # input placeholder

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print(); # input placeholder

JCIrblkyVikqISM3

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print(); # input placeholder

No error was evoked: this confirms that the parameter values give a stationary invertible time series.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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print(); # input placeholder

JCErOScpPihHIyEiKA==

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<Text-field style="Heading 2" layout="Heading 2">fGn parameters</Text-field>

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print(); # input placeholder

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<Text-field style="Heading 2" layout="Heading 2">Model 3 parameters</Text-field>

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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<Text-field style="Heading 1" layout="Heading 1"><Font size="16">Check residuals for autocorrelation</Font></Text-field>

The procedure Model3RSS was temporarily modified to assign the residuals to a global variable k2.

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

XUJGQTUzQjQxMjdGNThERTg=

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Thus, the residuals and the squared residuals exhibit negligible first-order autocorrelation.

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print(); # input placeholder

JCErKzljcUIhIig=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 3" italic="false" size="18" layout="Heading 3"><Font italic="false" size="16">Compare with ARMA(4,1)</Font></Text-field>

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print(); # input placeholder

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print(); # input placeholder

JCIrOyRmVlIiISIp

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRitGK0Yv

Thus, Model 3 is vastly better than ARMA(4,1), even after allowing for the extra parameter it has.

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The following shows what happens if we allow shifting HadCRUT: there is negligible improvement.

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print(); # input placeholder

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print(); # input placeholder

JCIpOSVlaSQhIik=

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<Text-field style="Heading 1" layout="Heading 1">IPCC model of temperatures</Text-field>

Among the 1000 time series, the first series is not generated using the three main models, but using the IPCC model,

with a fixed trend of 1 per century.

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print(); # input placeholder

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print(); # input placeholder

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<Text-field style="Heading 1" layout="Heading 1">Encrypt answer</Text-field>

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

SSV0cnVlRyUqcHJvdGVjdGVkRw==

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<Text-field style="Heading 1" layout="Heading 1">Code to generate the 1000 series</Text-field>

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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