Principles and risks
of forecasting (pdf)

Famous
forecasting quotes

How to move data around

Get to know your data

Inflation adjustment
(deflation)

Seasonal adjustment

Stationarity and differencing

The logarithm transformation

**Inflation adjustment**

**Inflation
adjustment**,
or "deflation", is accomplished by *dividing a monetary time series
by a price index*, such as the **Consumer Price Index** (CPI). The
deflated series is then said to be measured in "constant dollars,"
whereas the original series was measured in "nominal dollars" or
"current dollars." Inflation is often a significant component of
apparent growth in any series measured in dollars (or yen, euros, pesos, etc.).
By adjusting for inflation, you uncover the *real growth,* if any.
You also may stabilize the variance of random or seasonal fluctuations and/or
highlight cyclical patterns in the data. Inflation-adjustment is not
always necessary when dealing with monetary variables--sometimes it is simpler
to forecast the data in nominal terms or to use a logarithm
transformation for stabilizing the variance--but it is an important tool in the
toolkit for analyzing economic data.

The
Consumer Price Index is probably the best known US price index, but other price
indices may be appropriate for some data. The **Producer Price Index** and
the **GDP Implicit Price Deflator** are some other commonly used indices,
and numerous industry-specific indices are also available. The U.S.
Bureau of Economic Analysis compiles a wide array if "chain-type"
price indices for various kinds of personal consumption goods. A
chain-type index is one that is obtained by chaining together monthly,
quarterly, or annual changes in relative prices that are adjusted for changes
in the composition of the commodity basket, so as to reflect changes in
consumer tastes. (For more details on chain-type indices, see the following
article.)

Use of the
"correct" price index is important if you are interested in knowing
the exact magnitudes of trends in real terms and/or if the relevant price
history has undergone sudden jumps or significant changes in trend rather than
consistent increases over time. However, deflation by a
general-purpose index such as the CPI is often adequate for rough estimates of
trends in real terms when doing exploratory data analysis or when fitting a
forecasting model that adapts to changing trends anyway. Keep in mind
that when you deflate a sales or consumer expenditures series by a general
index such as the CPI, you are not necessarily converting from dollars spent to
units sold or consumed, rather, you are converting from dollars spent on one
type of good to equivalent quantities of *other consumer goods* (e.g.,
hamburgers and hot dogs) that could have been purchased with the same
money. Sometimes this is of interest in its own right because it reveals
growth in relative terms (i.e., relative to the other goods).

Here is a
graph of the auto sales in nominal dollars plotted alongside the CPI over the
last 25 years, where the CPI has been scaled so that the January 1990 value is
1.0.

Now here
is a graph of auto sales divided by (i.e. deflated by) the CPI. Note that much
(though not all) of the upward trend has been removed, accentuating the
seasonal and cyclical components of the data. The recessionary periods in the
mid-1970's, early 1980's, and early 1990's are especially evident:

Notice
that to perform the inflation adjustment in Statgraphics, you merely have to
type the expression AUTOSALE/CPI as the input variable (assuming that AUTOSALE
and CPI are pre-existing variables). If you wanted to perform the same
calculation on a spreadsheet, it would look like this:

When
looking at descriptions of time series in Economagic or other data sources, the
identifier "$" or "dollars" means the series is in *nominal*
dollars (i.e.,* not* inflation-adjusted). An identifier such as "1990
dollars" or "1990 $" means that the series is in *constant*
(inflation-adjusted) dollars, with 1990 taken as the reference point. For
modeling purposes, the choice of a reference point doesn't matter, since
changing the reference point merely multiplies or divides the whole series by a
constant. To move the reference point to a different base year, you would just
divide the whole price index series by the current value of the index at the
desired reference date. However, the parameters of a model are easier to
interpret if the *same* reference point is used for all inflation
adjustments. The thing you wish to avoid at all costs is having some variables
which *are* inflation adjusted and others which *aren't*: this will
introduce apparent nonlinear relationships which are merely artifacts of
inconsistent units.

The
following spreadsheet illustrates how you could adjust the auto sales series to
1970 dollars instead of 1990 dollars. First, the CPI series is divided through
by its original value in January 1970, to obtain a new consumer price index
series called CPI70 in which the 1970 value is equal to 1.0. Then the auto
sales series is divided by the CPI70 index:

Of course,
the graph of the auto sales series in 1970 dollars would look identical to the
graph in 1990 dollars: only the axis scale numbers would change.

Finally,
remember that inflation adjustment is only appropriate for series which are
measured in units of money: *if the series is measured in number of widgets
produced or hamburgers served or percent interest, it makes no sense to deflate*.
If a non-monetary series nonetheless shows signs of exponential growth or
increasing variance, it may be useful to try a logarithm transformation
instead.