18 May 1999

Example 1.  Graphs of differences of accumulating sums of squared
            "out of sample" regARIMA model forecast errors are useful
            for comparing two models or two adjustment approaches. 
            These sums are produced by the history spec. This example 
            uses these measures of forecast performance to compare 
	    two aproaches to Easter effect estimation for the series 
            U.S. Retail Sales of Shoes.
 
            The first approach is the x11easter option of the x11 spec. 
            The second is the easter[8] variable of the regression 
            spec.  The spec files shoersm1.spc and shoersm2.spc 
            generate the accumulating sums from the two approaches. 
            
            The graph of the differences of the sums (available via 
            X-12-Graph) indicates that the regARIMA Easter model 
            should be preferred.
            (Use the -g execution flag so files are available for 
            X-12-Graph.)

            As a further excercise, modify shoersm1.spc to produce 
            a new spec file that yields easter effects estimated from 
            easter[8] in the x11regression spec. Compare the forecast 
            performance of this approach with the performance of each 
            of the other two approaches.


Example 1:  shoers.mta   

The metafile that runs the two spec files for this example.

shoersm1
shoersm2



# Example 1:  shoersm1.spc 

# The spec file that generates the history of the out of sample forecast 
# errors when easter effects and their forecasts are obtained from 
# the x11easter option of the x11 spec. The resulting X-11 Easter factors  
# are removed from the original series before the regARIMA model 
# is estimated. The regARIMA model forecasts are multiplied by easter
# factor forecasts to obtain forecasts for the original series.

series {
 title="Shoe Store Sales with X11 Easter Adjustment"
 file = 's0b566.dat'
 format = '2L'
 name='S0B566'
 span = (1972.1,)
 modelspan=(1983.1,)
}
transform { 
 function = log
}
regression { 
 variables = td
}
arima {
 model = ( 0 1 1 ) ( 0 1 1 ) 
} 
estimate { }
x11 {
 seasonalma = s3x5
 x11easter=yes
 save=h1
 appendfcst=yes
}
history {
 start=1991.1 
 estimates=(fcst)
}

# Example 1:  shoersm2.spc 

# The spec file that generates the history of the out of sample 
# forecast errors when easter[8] is included in the regARIMA model.

series {
 title="Shoe Store Sales with Regression Easter[8]"
 file = 's0b566.dat'
 format = '2L'
 name='S0B566'
 span = (1972.01,)
 modelspan=(1983.1,)
}
transform { 
 function = log
}
regression { 
 variables = (  td easter[8]  )
}
arima { 
 model = ( 0 1 1 ) ( 0 1 1 ) 
} 
estimate { 
}
outlier { types = all }
x11 {
 seasonalma = s3x5
}
history {
 start=1991.1 
 estimates=(fcst sadj)
}