<![if !vml]><![endif]>Data concepts
Principles and risksof forecasting (pdf)
Famousforecasting quotes
How to move data around
Get to know your data
Inflation adjustment(deflation)
Seasonal adjustment
Stationarity and differencing
The logarithm transformation
Inflation adjustment
Inflationadjustment,or "deflation", is accomplished by dividing a monetary time seriesby a price index, such as the Consumer Price Index (CPI). Thedeflated 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 ofapparent 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/orhighlight cyclical patterns in the data. Inflation-adjustment is notalways necessary when dealing with monetary variables--sometimes it is simplerto forecast the data in nominal terms or to use a logarithmtransformation for stabilizing the variance--but it is an important tool in thetoolkit for analyzing economic data.
The ConsumerPrice Index is probably the best known US price index, but other price indicesmay be appropriate for some data. The Producer Price Index and the GDPImplicit Price Deflator are some other commonly used indices, and numerousindustry-specific indices are also available. The U.S. Bureau of EconomicAnalysis compiles a wide array of "chain-type" price indices forvarious kinds of personal consumption goods. A chain-type index is onethat is obtained by chaining together monthly, quarterly, or annual changes inrelative prices that are adjusted for changes in the composition of thecommodity basket, so as to reflect changes in consumer tastes. (For moredetails on chain-type indices, see the following article.)
Thefollowing chart shows price indices for a variety of products and services overthe period from 1997 to 2010, all scaled to a value of 100% in 1997. There are some strikingdifferences: the price ofgasoline has experienced large downward as well as upward movements due toshocks 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-stepfashion, and the price of computers has shown an exponential decline rather than exponentialgrowth. (The ordering of the seriesin the legend is the same as their rankings in 2010, except that the all-itemsindex should be ranked below rather than above fast food.)
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Use of anappropriate price index is important if you are interested in knowing the truemagnitudes of trends in real termsand/or if the relevant price history has undergone sudden jumps or significantchanges in trend rather than consistent increases over time.However, deflation by a general-purpose index such as the CPI is often adequatefor rough estimates of trends in real terms when doing exploratory dataanalysis or when fitting a forecasting model that adapts to changing trendsanyway. Keep in mind that when you deflate a sales or consumerexpenditures series by a general index such as the CPI, you are not necessarilyconverting from dollars spent to units sold or consumed, rather, you areconverting from dollars spent on one type of good to equivalent quantities of otherconsumer goods (e.g., hamburgers and hot dogs) that could have beenpurchased with the same money. Sometimes this is of interest in its ownright because it reveals growth in relative terms, compared to prices of othergoods.
Here is thegraph of U.S. total retail sales in nominal dollars ($millions) plotted alongside the CPI forthe period from January 1992 to August 2015, where the CPI has been scaledso that the average value in 2010 is 100:
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Next, hereis a graph of retail sales divided by (i.e. deflated by) the CPI. The trend that remains is real growth. The seasonal pattern and the magnitudeof the drop in sales during the Great Recession stand out more clearly whendisplayed in real terms:
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Thefollowing screen shot of the spreadsheet shows how the process of adjusting theretail sales to 2010 dollars was carried out here. The U.S. all-city-average CPI wasobtained from a public source (Economagic.com) and adjusted to 2010 dollars bydividing it by the average 2010 value and then multiplying by 100. (It is conventional to scale it to avalue of 100 in the base year.) Theinflation-adjusted values were obtained by dividing the original sales valuesby the 2010 CPI and then multiplying by 100. For example, 206344 = (130683/63.33)x100.
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When lookingat descriptions of time series obtained from government or commercial datasources, the identifier "$" or "dollars" means the seriesis in nominal dollars (i.e., not inflation-adjusted). Anidentifier such as "2010 dollars" or "2010 $" means thatthe series is in constant (inflation-adjusted) dollars, with 2010 takenas the reference point. For modeling purposes, the choice of a reference pointdoesn't matter, since changing the reference point merely multiplies or dividesthe whole series by a constant. To move the reference point to a different baseyear, you would just divide the whole price index series by the current valueof the index at the desired reference date. However, the parameters of a modelare easier to interpret if the same reference point is used for allinflation adjustments. The thing you wish to avoid at all costs is having somevariables which are inflation adjusted and others which aren't:this will introduce apparent nonlinear relationships which are merely artifactsof inconsistent units.
Finally, rememberthat inflation adjustment is only appropriate for series which are measured inunits of money: if the series is measured in number of widgets produced orhamburgers served or percent interest, it makes no sense to deflate. If anon-monetary series nonetheless shows signs of exponential growth or increasingvariance, it may be useful to try a logarithm transformationinstead.
Go on to next topic: Seasonal adjustment
