[SF]Interpretation of a Stochastic Forecast
Goal of a Stochastic Forecast
A population forecast is intended to be useful in the analysis
and planning of social and economic systems such as pensions,
health care, education, child care, marketing, investment etc. As a
tool in decision making the forecast is a summary of our knowledge
of past trends and likely future developments. Given that the
predictive value of our current knowledge decreases rapidly as we
look further into the future, a characterization of the increasing
uncertainty is an essential part of the forecast.
Forecast users cannot, themselves, assess the uncertainty of
forecasts. A general finding is that even sophisticated users tend
to underestimate uncertainty. Stochastic forecasts are particularly
useful when inform the users about the possibility of such future
developments that are not the foremost in the minds of the planners
and politicians.
Predictive Distributions
The uncertainty of the UPE forecast is described in terms of
probabilities. For each of the 47 forecast years, we have 101
agegroups for both sexes. Or, there are 47×101×2 random variables
representing population size in a given year, at a given age, for a
given sex. A predictive distribution of future population
is the joint probability distribution of these random variables.
This distribution takes the place of the conventional projection
variants and scenarios.
In practice, predictive distributions are first specified for
the vital processes of fertility, mortality, and
migration. Then, cohortcomponent bookkeeping is
used to derive the induced predictive distribution for future
population.
The term stochastic population forecast refers to the
stochastic process aspects of the predictive distribution. The term
probabilistic population forecast emphasizes the fact that
we use probabilities rather than conventional variants or scenarios
to describe uncertainty. Mathematically, they are equivalent to the
notion of a predictive distribution.
Subjective Interpretation and External Calibration
Since the events whose probabilities we consider only occur once
(e.g., the female population of a country, in age 35, in the
beginning of year 2025, obtains a unique value in the course of
history), the probabilities cannot be interpreted as relative
frequencies. They are best understood subjectively, as
representing the degree of uncertainty we now feel concerning the
size of future population.
On the other hand, a predictive distribution allows us to make
(infinitely) many probability statements. When the future has
unfolded, it is possible to evaluate whether or not they have given
an appropriate description of uncertainty. We may refer to this as
external calibration of predictive distributions. The
practical difficulty in external calibration, is that errors in
forecasting are typically highly correlated, so any statistical
evaluation of past forecasts may have low statistical power. In
addition, the waiting time until all forecast years have been
followed up, may be prohibitively long.
Subjective probabilities can vary from one individual to
another. However, for a predictive distribution to be generally
useful, it is necessary that the probabilities can be characterized
in relatively objective terms. Our goal has been to produce
predictive distributions that have an empirical, statistical
foundation.
Medians and the Spread Around Them
In general, we use medians as the location parameter of
the predictive distributions. They represent our best guess as to
the future values of the vital processes, by age and sex. Thus, we
should be able to interpret the medians as giving the best
summary of future from what we have learned from the past. We
formulate the medians based on estimates of current values, time
series models and judgment.
The spread of the distribution around the median should give a
realistic indication of forecast uncertainty the user of the
forecast should expect. The starting point of the
specification of the spread is the uncertainty observed in the
past. We determine the level of past uncertainty using the errors
of actual past forecasts, errors of statistical timeseries models,
and errors of simple baseline (or naive) forecasts. Judgment is
used to adjust such estimates up or down so that the desired
interpretation is achieved.
Last updated
17.9.2004
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