The diffusion indexes and the composite indexes of business cyclical
indicators are summary measures designed to facilitate the business cycle
analysis by aggregating the behavior of a group of economic time series
that represent widely differing activities or sectors of the economy.
Both the diffusion indexes and the composite indexes consist of three
indexes: leading index, which combines a group of economic time series
that tend to precede business cycle turning paints; coincident index, which
combines those that tend to coincide with turning points; and lagging index,
which combines those that tend to lag turning points.
1. Diffusion Indexes of Business Indicators
(How to evaluate the diffusion indexes)
In order to judge the current business cycle phase and forecast the
turning points of the business cycle, the diffusion indexes measure in
percentage form how many series among the entire selected series are showing
an increase over a given time span. It is hoped that the following point
are kept in mind when the diffusion indexes are used in the analysis of
economic fluctuations:
(1) Duration
If the duration of increase or decrease of economic activities is very
short, it is not considered to be an expansion or contraction.
(2) Dispersion
The diffusion indexes represent the extent to which business fluctuations
spread across various sectors of the economy. When an upward or downward
movement transmits itself into most of the sectors, it is considered to
be the turning point of a business cycle.
In judging a business cycle phase, it is usually checked whether the
diffusion indexes are above or below 50 percent. But in recent years, movements
in the differing sectors sometimes differ widely. Hence, it would be necessary
to confirm that the dispersions of business fluctuations is sufficiently
wide so that the diffusion indexes are near zero (in the case of recession)
or 100 (in the case of recovery) percent.
(3) Amplitude of the fluctuation of economic activities
Economic fluctuations are regarded as business cycles only when they
fluctuate with certain amplitude. For example, even if the level of economic
activity only stops declining without reincreasing afterward, it may not
be appropriate to consider it to be a recovery. Similarly, if the level
of economic activities declines a little but remains high, it many not
be appropriate to consider it to be a recession.
To measure the amplitude of recessions and recoveries, it is recommended
that references are made to the composite indexes explained below. Because
the diffusion indexes are constructed by aggregating the directions of
changes of the selected series, they do not represent the amplitude of
business cycle fluctuations.
(How to construct the diffusion index)
First, the direction of change for the month in each series is decided
by a comparison of the monthly figure with that of three months ago and
is given a plus(+) for the month if the monthly figure shows an increase,
or a minus(-) if it shows a decrease, or zero(0) if unchanged .
Secondly, the number of pluses on the same column in The Direction-of-Change
Table are counted for the month (In case of zero, it is counted as one-half
rising); then, the number of the pluses is divided by the total number
of the components. The proportion of the rising series, in short, is the
diffusion index.
2. Composite Indexes of Business Indicators
(How to evaluate the composite indexes)
For the main purpose of measuring the amplitude of the fluctuations
of economic activities, the composite indexes are constructed by aggregating
the percentage changes of the selected series. They are represented with
the average of their 1995 values as 100.
Generally speaking, when the composite coincident index is rising,
we can regard it as indicating expansion, and when declining, as indicating
contraction. Therefore, the turning points of the business cycle exist
somewhere around those of the composite coincident index. Moreover, we
can always observe the intensity of business activities by the underlying
movement of the composite indexes.
(How to construct the composite index)
Step1: Let xi(t) be the symmetrical percent change from
month t-1 to month t for component i, Then
,
where i and t are defined as above.
,
the standard deviation;
,
and the normalised change Zi(t), where
,
,
,
and K is the number of components.
When leading and lagging indexes are composed, the ;
; for coincident index is used in place of the ;
for each index from the viewpoint that it is desirable that the trend component
in all three Composite Indexes (leading, coincident and lagging) is the
same.
Step4: the I(t) are cumulated by applying the formula,
Finally ,this index is rebased so as to make the average of the values in 1995=100
Reference Material: Reference Dates of Twelve post-War Cycles
The Reference Dates of Business Cycle
| Peak (By Month) | Trough (By Month) | Peak (By Quarter) | Trough (By Quarter) |
| Jun. 1951 | Oct. 1951 | 2Q 1951 | 4Q 1951 |
| Jan. 1954 | Nov. 1954 | 1Q 1954 | 4Q 1954 |
| Jun. 1957 | Jun. 1958 | 2Q 1957 | 2Q 1958 |
| Dec. 1961 | Oct. 1962 | 4Q 1961 | 4Q 1962 |
| Oct. 1964 | Oct. 1965 | 4Q 1964 | 4Q 1965 |
| Jul. 1970 | Dec. 1971 | 3Q 1970 | 4Q 1971 |
| Nov. 1973 | Mar. 1975 | 4Q 1973 | 1Q 1975 |
| Jan. 1977 | Oct. 1977 | 1Q 1977 | 4Q 1977 |
| Feb. 1980 | Feb. 1983 | 1Q 1980 | 1Q 1983 |
| Jun. 1985 | Nov. 1986 | 2Q 1985 | 4Q 1986 |
| Feb. 1991 | Oct. 1993 | 1Q 1991 | 4Q 1993 |
| May. 1997 | Jan. 1999 | 2Q 1997 | 1Q 1999 |
| (Oct. 2000) | (4Q 2000) |