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 of "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.)

The
following chart shows price indices for a variety of products and services over
the period from 1997 to 2010, all scaled to a value of 100% in 1997. There are some striking
differences: the price of
gasoline has experienced large downward as well as upward movements due to
shocks to the world economy, tobacco prices have risen in large part due to taxation,
the price of a college education has gone up dramatically in stair-step
fashion, and the price of computers has shown an exponential *decline* rather than exponential
growth. (The ordering of the series
in the legend is the same as their rankings in 2010, except that the all-items
index should be ranked below rather than above fast food.)

Use of an
appropriate price index is important if you are interested in knowing the true
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, compared to prices of other
goods.

Here is a
graph of the auto sales in nominal dollars plotted alongside the CPI for the 25
years from 1970 to 1995, 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:

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 obtained from government or commercial 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.

Go on to next topic: Seasonal adjustment