PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

MODELING FINANCIAL SCENARIOS 195(http://www.bls.gov) and ran several regressions of this type toestimate ·q and ¹ q . One specific concern of this data was that individualmonthly CPI levels might contain self-correcting errorsthat would bias the regression coefficients. For example, if theCPI of September 2004 was overstated and then corrected in thefollowing month, then inflation in September would temporarilyappear “high” while the subsequent inference of monthly inflationwould appear “low.” If the time series of CPI containedany errors of this type, the resulting mean reversion strength andvolatility parameters may be overstated. Given the noisy fluctuationsin monthly data, we selected the parameters for the inflationprocess by looking at annual regressions. By calculating thechange in CPI over the course of a year, the inflation rate wouldappear less volatile.The often-cited time series of CPI uses a base period (i.e.,resets the index value at 100) between the years 1982 and 1984.Given the fact that the CPI level is reported only to the first decimalplace, using the current base does not lend itself to capturingminor changes in inflation in the first half of the 20th century; asmall change in CPI may lead to large swings in inflation whenthe level of the index is low. The only other publicly availableseries reported on the old base level (1967 = 100) is the one thatis not seasonally adjusted, U.S. city averages, all items. 6The annual rate of inflation was measured asq t =ln CPI t, (3.7)CPI t¡1where CPI t is the reported index value for year t and CPI t¡1 isthe prior year’s reported index value of the same month. We rantwo annual regressions: (1) all available data and (2) the yearsafter World War II.6 Often in economic data, seasonal adjustments are required to remove persistent cyclicalfactors that may affect raw (unadjusted) values. Examples of seasonal factors that mayhave an impact on CPI include effects from climatic changes, holidays, and productioncycles.