                                                     12 November 1998

Example 7:  The specs in this example demonstrate some of the strategies 
            we have found for dealing with residual spectrum peaks.  Some 
            of the strategies listed below don't have an associated example 
            spec file.

            Strategies Against Spectrum Peaks at Seasonal Frequencies in 
            the spectrum for RegARIMA Residuals --
            (1)  Change the ARIMA model, e.g., add a seasonal AR term.
            (2)  Change the regressors.  
                 (a)  Remove fixed seasonal regressors and add a seasonal 
                      ARIMA model, such as (0 1 1)12.
                 (b)  Add outliers that are just below the critical value.
            (3)  Change the data, e.g., remove all but the last 8-10 years 
                 of the series.

            Strategies Against Spectrum Peaks at Trading Day Frequencies 
            in the spectrum for RegARIMA Residuals, the seasonally adjusted 
            data, or the irregulars --
            (1)  Add TD variables to the regression if none were included 
                 or if those tried were rejected by an AIC test.  (Setting
                 insignificant coefficients to zero can sometimes change the 
                 aictest result from rejection to acceptance.)
            (2)  Choose a different type of TD regressor, such as a stock 
                 trading day variable (tdstock), a weekend/weekday trading 
                 day variable (td1coef), or a user-defined trading day 
                 variable.  You may also want to try a change-of-regime 
                 version of any of the trading day variables.

            Suggested graphs:
            A graph of the original series to help find a shorter span,
            spectrum graphs, and sum of squared forecast error history graphs.


            The Italian Export Quantity Index (CETGENGQ) --

            The spec file cetg0.spc contains a default run of the Italian 
            Export Quantity index.  The aictest rejects trading day.  The 
            spectrum of the both the RegARIMA residuals and the irregular 
            contains trading day peaks.  (This series has already been 
            shortened from 1980.jan to 1986.jan.  Remove the span 
            statement and graph the original series to see why the series 
            was shortened.)

            The aictest for trading day rejects trading day based on the AIC.  
            We compared all the trading day options (Flow TD, Stock TD, 
            Weekday/Weekend TD, and No TD) using AIC history graphs and Sum 
            of Squared Forecast Error graphs in X-12-Graph.  Stock TD had 
            the lowest out-of-sample forecast error.  AICs for the stock 
            trading day can be improved by using the b option in the 
            regression spec and fixing some of the coefficients to zero.  
            The example spec file with Stock trading day added is cetg1.spc.

            With the trading day included, there are both seasonal and 
            trading day peaks in the RegARIMA residuals.  We had some 
            success in reducing the size of the seasonal peak by adding 
            a seasonal AR(1) term to the model.  However, even without the 
            seasonal AR(1) term, when we added regressors for the outliers 
            with the largest absolute t-values, the seasonal peak was 
            eliminated.  Our final options are in cetgengq.spc.

            US Single Family Housing Starts for Northeast and Midwest Regions --

            ne1f0.spc shows a run for the Northest Single Family Housing 
            Starts series.  A seasonal peak was found in the RegARIMA
            residuals.  A graph of both series suggests that the series has 
            changed significantly in recent years.  Shortening the series 
            changes the ARIMA model coefficients and eliminates the seasonal 
            spectrum peak. 

            mw1f0.spc shows a run for the Midwest region.  A trading day peak
            was found in the RegARIMA residuals.  There is evidence of 
            deminishing trading day effects in the later part of the series.
            A change-of-regime trading day regressor eliminates the
            trading day spectrum peak.



# Example 7:  cetgengq.spc

# Our final settings for this series.


series{
  name="CETGENGQ" 
  start=1980.1
  period=12
  file="cetgengq.dat"
  title="CETGENGQ: Airline Model with Outliers and Stock TD"
  span=(1986.1,)
  decimals=1
}
transform{function=log}
regression{
  variables=(tdstock[31] 
    ao1987.3  ls1987.7  ao1988.1  ao1993.8    )
  b=(0. 0.0f 0.0f 0. 0. 0.0f
     0. 0. 0. 0.)
}
arima{model=(0 1 1)(0 1 1)}
estimate{}
check{print=all  savelog=lbq}
forecast{maxlead=24  print=none}
x11{
  savelog=(q q2 m7 m10 m11)
}
slidingspans {
  print=(default +pcy +suy)
  savelog=percent
}
#history{
#  estimates=(sadj sadjchng trend)
#  fixmdl=no
#  start=1994.1
#}
