ON MEASURING THE INSTABILITY OF TIME SERIES DATA
| DOI | http://doi.org/10.1111/j.1468-0084.1979.mp41003006.x |
| Date | 01 August 1979 |
| Author | JAMES E. DUGGAN |
| Published date | 01 August 1979 |
ON MEASURING THE INSTABILITY OF TIME SERIES DATA
By JAMES E. DUGGAN*
1. INTRODUCTION
In a recent article in the BULLETIN, Cuddy and Della Valle (C-D) (1978)
address the questions of what is meant by instability in time series data and how
should it be measured and compared across time series. After briefly reviewing
several existing approaches, the authors present a 'general measure' of instability
that essentially involves an adjustment to the widely used coefficient of variation
(CV). Following an empirical application to commodity prices, in which they
compare values of their 'corrected coefficient of variation' and the standard CV,
C-D offer a three-part selection rule that is centred on the significance of the
adjusted coefficient of determination from a regression of the data (or log of) on a
linear time trend.
The purpose of this paper is to improve further the methodology for measuring
time series instability by proposing an alternative approach that is more general
and statistically superior to the measure suggested by C-D. The paper begins with
a definition of instability that is linked directly to the concept of predictability and
appropriately labelled inherent variability: the less predictable is a series, based on
its own past history, the more inherently variable or unstable it is. By invoking
the concept of predictability, an operational measure of instability can be derived
that has several distinct advantages over other measures: (1) a general principle of
variability is offered that is common to all applications; (2) the derivation of its
measurement is based on sound statistical theory and avoids some obvious pitfalls
of other measures; (3) the empirical methodology applies to data either seasonally
adjusted or not seasonally adjusted; and (4) its empirical derivation is a by-product
of a thorough analysis of the time series data that is likely to be highly desirable in
any case.
The next section explains in more detail the meaning of inherent variability of
time series. The third section illustrates how it may be transformed into a
'coefficient of variation,' thereby allowing comparisons of inherent variability
between and among series. The fourth section provides an empirical example,
using seasonally unadjusted data on monthly employment data for the US, the
State of Rhode Island, and eight industry divisions in the State of Rhode Island
over the postwar period (1948(1)-1 975(12)). The particular time series are used
for illustrative purposes only and reflect an interest in the important problem of
assessing relative employment fluctuations; however, the analysis is intended for
all types of time series data, including commodity prices as used in the C-D paper.
The final section offers some concluding remarks.
* The views expressed in this paper are the author's alone and not necessarily those of the US Bureau
of Labor Statistics. Thanks are due William Bailey, Stephen Baldwin and Joe Stone for helpful
comments. 239
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