Airline Passengers 

The following data contains the monthly total number of US international airline passengers (in thousands) from January 1949 to December 1960.

In[1]:=

X passengers = TemporalData[TimeSeries, {CompressedData[" 1:eJwt0s0rplEYB+AXGzX5SBkbmymWaCxE0/gb0GRjskARYqLIwpQyWFDoxYoy ZIGFMI2FEk1JaJKNbEX52rBSFq439+LqnM7z63efp86npu66rvREIpHGJD/o Y5ghBhglGcbopy1yvfxkInKDzLAaFvhFD+NMMcsmS6zH/jDs8JtpVlhjm33+ 8JdLbnjijL3oOeBfeOCea57J9IO5PNqfR+cRJ+xG9oq7yJZSTEbae8dxdKVm 3vLBeRbZfKGTBirJizkfrYXk85UqquljnhmaKScn1lRXCS18j+8rnHFOMuZ8 poZv0dke+Q62uOcl8q1UUEsb9cwyzjIXFHkEZfy3n4u+1P0WGWWJ08gWyKUe TSOvcT7CBm9ZnFBB "], { TemporalData`DateSpecification[{1949, 1, 1, 0, 0, 0.}, {1960, 12, 1, 0, 0, 0}, {1, "Month"}]}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {MetaInformation -> { "Source" -> "Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. \ (1994) Time Series Analysis, Forecasting and\nControl. Second \ Edition. New York: Prentice-Hall.", "Description" -> "International Airline Passengers: Monthly \ Totals (Thousands of Passengers) January 1949 - December 1960"}}}, True, 10.];

Split the data at January 1958.

In[2]:=

X before1958 = TimeSeriesWindow[passengers, {Automatic, "December 1957"}]; since1958 = TimeSeriesWindow[passengers, {"January 1958", Automatic}];

In[3]:=

X p = DateListPlot[{before1958, since1958}, Joined -> True, PlotLegends -> {"Before 1958", "After 1958"}]

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Fit a time series model to the airline passenger data before 1958.

In[4]:=

X tsm = TimeSeriesModelFit[before1958]

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The forecast from 1958 to 1961 compared to the actual data.

In[5]:=

X DateListPlot[{before1958, since1958, Table[{t, tsm[t]}, {t, DateRange["January 1958", "December 1960", "Month"]}]}, Joined -> True, PlotLegends -> {"Before 1958", "After 1958", "Forecast"}]

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