appears to have been overlooked previously.)^24 For example, exactly zero
EPS (or change in EPS or forecast error) occur with nontrivial probability
because of the rounding (as does any specific value like one penny). How-
ever, a zero remaps to zero after deflation compared to, for instance, a one-
penny EPS that can remap into a relatively large or small number depending
on the deflator. Thus, deflation can lead to a spurious buildup in the density
at zero, a critical area of interest for our study. In simulations not shown,
this problem proves significant under conditions where EPS is rounded off
to the nearest penny (as in practice).
Fortunately, if we exclude the extreme firms in terms of price, then defla-
tion to correct for possible heterogeneity proves unnecessary for the impor-
tant variables related to EPS that we study. Figure 18.4 shows the medians
(represented by hollow symbols) and interquartile ranges (represented by
corresponding solid symbols which are connected) of the important vari-
ables as a function of centiles of price per share.
648 DEGEORGE, PATEL, ZECKHAUSER
Figure 18.4. Medians and interquartile ranges for EPS, FERR, and ∆EPS as a func-
tion of centiles of price per share.
(^24) This problem is analogous to the “aliasing problem” in the literature on the spectral
analysis of time-series data (e.g., see Koopmans 1974, ch. 3). The classic aliasing problem
arises when the spectrum of interest is a continuous-time series but the available sample was
sampled at discrete intervals. In this situation, either lack of prior knowledge of the specific
bounds of the frequency interval in which the spectrum is concentrated, or an inability to sam-
ple often enough, results in accurate estimates of the sampledprocess spectrum providing poor
or misleading estimates of the original spectrum. In our setting, the estimate of the probability
density function risks distortion owing to the initial rounding off (discretization) of EPS and
any subsequent renormalization.