Page 143 - Contributed Paper Session (CPS) - Volume 5

CPS1159 Philip Hans Franses et al.
To evaluate the quality of the forecasts from these forecasters, one often takes
the average quote (the consensus) or the median quote, and sometimes also
measures of dispersion like the standard deviation or the variance are
considered. The latter measures give an indication to what extent the
forecasters disagree. Recent relevant studies are Capistran and Timmermann
(2009), Dovern, Fritsche, and Slacalek (2012), Lahiri and Sheng (2010), Laster,
Bennett, and Geoum (1999), and Legerstee and Franses (2015). Reasons for
disagreement could be heterogeneity across forecasters caused by their
differing reactions to news or noise, see Patton and Timmermann (2007),
Engelberg, Manski and Williams (2009), and Clements (2010).
Recently, Clements (2017) suggested that there might be another reason
why forecasters disagree, and that is, that they may target at different vintages
of the macroeconomic data. Some may be concerned with the first (flash)
quote, while others may have the final (say, after 5 years) value in mind. The
problem however is that the analyst does not know who is doing what.
The question then becomes how one should deal with the MZ regression.
Of course, one can run the regression for each vintage on the mean of the
forecasts. But then still, without knowing who is targeting what, it shall be
difficult to interpret the estimated parameters in the MZ regression. At the
same time, why should one want to reduce or remove heterogeneity by only
looking at the mean?
To alleviate these issues, in this paper we propose to keep intact the
heterogeneity of the realized values of the macroeconomic variables as well
as the unknown heterogeneity across the quotes of the professional
forecasters. Our proposal relies on the notion to move away from scalar
measurements to interval measurements. Such data are typically called
symbolic data, see for example Bertrand and Goupil (1999) and Billard and
Diday (2007). The MZ regression for such symbolic data thus becomes a so-
called Symbolic Regression.
The outline of our paper is as follows. In the next section we provide more
details about the setting of interest. For ease of reading, we will regularly refer
to our illustration for annual USA real growth rates, but the material in this
section can be translated to a much wider range of applications. The following
section deals with the estimation methodology for the Symbolic Regression.
We will also run various simulation experiments to examine the reliability of
the methods. Next, we will apply the novel MZ Symbolic Regression to the
USA growth rates data and compare the outcomes with what one would have
obtained if specific vintages were considered. It appears that the Symbolic MZ
Regression is much more informative. The final section deals with a conclusion,
limitations, and further research issues.

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