Filling in the Gaps for A Partially Discontinued Data Series
by James R. Knaub, Jr
.
Abstract:
Data on US coal production, imports, producer and distributor stocks, consumption,
exports, consumer stocks, and, by default, losses and unaccounted for coal, have been collected,
and, considering changes in stock levels, all data have been 'balanced' on a quarterly basis. That
is, the relationship between these variates is written as a single equation. These data have been
published in the Energy Information Administration (EIA) Quarterly Coal Report for more than
sixteen years. Producer and distributor stocks (p/d stocks) will no longer be collected on a
quarterly basis, due to budgetary constraints, but will be observed annually. The EIA still
wishes to publish these data quarterly, with 'estimates' given for p/d stocks for the first, second
and third quarters of each year, and the observed value given for the fourth quarter. (Note that
these "estimates" are actually "predictions." However, unlike the usual case with predictions, no
values will ever be observed for first, second or third quarter p/d stocks after 1997. Also, we are
only interested in a value to approximate the current conditions for each of these publications,
not forecasts of the future.)
This paper explores the use of weighted linear regression modeling, prediction and the variance
of the prediction error, and the combination of 'predictions' from different models, to help fill in
these unobserved p/d stock quarterly values in a reasonable manner, and provide estimated
standard errors. The procedures found here have substantial potential for use whenever one
might consider reducing the frequency of periodic data collection for an established data series.
Key Words:
linear regression; heteroscedasticity; regression weights; model; prediction;
combining estimators; standard error of the prediction error; SAS PROC REG STDI; missing
'time series' data
distribution, generated models; extreme distributions
Author:
James R. Knaub, Jr.,
james.knaub@eia.doe.gov
Editor:
Jan Beran
,
jberan@iris.rz.uni-konstanz.de
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