In
econometrics
Econometrics is the application of Statistics, statistical methods to economic data in order to give Empirical evidence, empirical content to economic relationships.M. Hashem Pesaran (1987). "Econometrics," ''The New Palgrave: A Dictionary of ...
, a dynamic factor (also known as a diffusion index) is a series which measures the
co-movement of many
time series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...
. It is used in certain
macroeconomic model
A macroeconomic model is an analytical tool designed to describe the operation of the problems of economy of a country or a region. These models are usually designed to examine the comparative statics and dynamics of aggregate quantities such as ...
s.
A diffusion index is intended to indicate
* the changes of the fraction of economic data
time series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...
which increase or decrease over the selected time interval,
* an increase or decrease in future economic activity,
* provide some correlation to the business sentiment of companies.
Formally
:
where
is the
vector
Vector most often refers to:
*Euclidean vector, a quantity with a magnitude and a direction
*Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism
Vector may also refer to:
Mathematic ...
of lagged factors of the
variables in the
matrix
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchise
** ''The Matrix'', a 1999 science-fiction action film
** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...
(T is the number of observations and N is the number of variables),
are the factor loadings, and
is the factor
error
An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'.
In statistics ...
.
History
Diffusion indexes were originally designed to help identify business cycle turning points.
Example
A diffusion index of monthly employment levels across industries measures the degree to which a growth in employment levels in a population is made up of growth in all industries versus sharp growth in just a few industries. In one published data series on that design, the diffusion index is computed from a panel of discrete time series by assigning a value of 0 to an observation if it is lower than its analog in the previous month, 50 if it is at the same level, and 100 if it has increased. The average of these component values for a given period over the time period is a diffusion index. Relative to the equation above, the underlying factors
are drawn from the values based on employment changes, and the diffusion index
works out to be the percentage of these employment counts that increased in the previous month. Some researchers have reported that a diffusion index of monthly manufacturing-sector employment is a leading indicator of turning points in the business cycle.
[Getz and Ulmer, pp 13-22.]
References
Literature
* Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory", ''Econometric Theory'', vol. 17(6), pages 1113-41.
* Getz, Patricia M. and Mark Ulmer
"Diffusion indexes: an economic barometer" ''
Monthly Labor Review
The ''Monthly Labor Review'' (''MLR'') is published by the U.S. Bureau of Labor Statistics (BLS). Issues often focus on a particular topic. Most articles are by BLS staff.
Annually since 1969, the Lawrence R. Klein Award has been awarded to autho ...
'', April 1990, Vol. 113, No. 4, pp. 13–22.
* Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes", ''Journal of Business & Economic Statistics'', vol. 20(2), pages 147-62.
Time series