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Global Warming

    
The global mean temperature in years 1880–2011 with the 1951–1980 mean removed:
Wolfram Language code: gmt = TemporalData[Automatic, {{{-0.32, -0.32, -0.23, -0.29, -0.3, -0.34, -0.33, -0.29, -0.36, -0.29, -0.18, -0.41, -0.29, -0.34, -0.35, -0.36, -0.28, -0.2, -0.16, -0.3, -0.19, -0.18, -0.28, -0.33, -0.37, -0.28, -0.22, -0.42, -0.36, -0.37, -0.3 ... 1, 0.06, 0.28, 0.33, 0.33, 0.21, 0.36, 0.14, 0.14, 0.14, 0.4, 0.31, 0.31, 0.42, 0.34, 0.36, 0.36, 0.49, 0.56, 0.49, 0.49, 0.62, 0.59, 0.44, 0.44, 0.57, 0.51}}, {{1880, 2011, 1}}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {}}, False, 9.];
Wolfram Language code: ListLinePlot[gmt, Filling -> -.5, AxesOrigin -> {1880, -.5}, ImageSize -> 300]
UnitRootTest suggests that there is a linear trend:
Wolfram Language code: UnitRootTest[gmt, Automatic, {"TestDataTable", All}]
Fit an ARIMAProcess model with a linear trend to the data:
Wolfram Language code: eproc = EstimatedProcess[gmt, ARIMAProcess[3, 1, 1]]
Simulate a possible scenario for the next 20 years using the ARIMA model, conditioned on past values:
Wolfram Language code: conditionalProc = Insert[eproc, gmt["Values"], -1]; future = RandomFunction[conditionalProc, {0, 19}];
Wolfram Language code: plotfuture = TimeSeriesShift[future, {{2012}}]; Labeled[ListLinePlot[Flatten[{gmt, plotfuture}, 1], Filling -> -.5, AxesOrigin -> {1880, -.5}, ImageSize -> 400], Column[{Style["Global Temperature Anomaly", 18, Bold, FontFamily -> "Helvetica"], Style["1880 to 2031", 14, Bold, FontColor -> Gray, FontFamily -> "Helvetica"]}], {{Top, Left}}]