ON MEASURING THE INSTABILITY OF TIME SERIES DATA: A COMMENT
| Date | 01 August 1979 |
| Published date | 01 August 1979 |
| Author | ALAN BROWN |
| DOI | http://doi.org/10.1111/j.1468-0084.1979.mp41003008.x |
ON MEASURING THE INSTABILITY OF TIME SERIES DATA:
A COMMENT
By ALAN BROWN
"Whether a given proposition is true or false, significant or meaningless,
depends on what question it was meant to answer."
R. G. Collingwood, An Autobiography, 1939.
What Professor Collingwood said about logical propositions 40 years ago holds
also, suitably rephrased, for statistical measures today. And it occurs to me that it
is as well to keep this in mind when considering the various proposals which have
been made in the last decade or so for the measurement of instability of economic
variables. Much discussion has taken place in the IMF, the World Bank and
UNCTAD: and in February 1978 the BULLETIN published a paper by Cuddy and
Della Valle, followed by the paper by Duggan in the present issue.
Noting that the simple coefficient of variation was the most commonly used of
all instability measures, Cuddy and Della Valle proposed a measure based on the
deviations from a linear or exponential trend, whichever is more appropriate. This
measure therefore included as a component of instability all cyclical fluctuations
present in the series, whether regular or irregular, as well as any component which
could be described as "white noise". Duggan has gone further, and by using Box
and Jenkins' techniques isolates the pure white noise component, which he regards
as the sole contributor to the instability of the series. This is because he defines
instability as equivalent to unpredictability.
I imagine that Cuddy and Della Valle would regard this as throwing out the
baby (cyclical variation) with the bath water (trend). It is clear that these writers
are approaching the problem from the point of view of UNCTAD, and of many
third-world countries looking through the eyes of UNCTAD. A third-world
country will regard its export revenues unstable whether the fluctuations in these
can be described as cyclical or due to white noise, unless perhaps the cyclical
movements are so regular that they can be confidently relied on to continue, a case
which rarely occurs. Behind such an approach lie specific questions related to
specific policy issues, such as the issue of buffer stocks policy.
It is equally significant that Mr. Duggan on the other hand is employed in the
US Bureau of Labour Statistics. He is interested first and foremost in the prediction
of time series, in particular of employment series. He wishes to reduce the errors
of his prediction to a minimum, and any technique, such as the Box and Jenkins'
technique, which removes all 'predictable' elements from the series, whether cyclical
or trend in nature, is to be used. From a semantic point of view it might be
questioned whether he is wise to consider this approach as equivalent to searching
for a generalised measure of instability, but perhaps we should not quibble too
much over semantic questions.
Two quotations will suffice to show what the writer has in mind when he
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