Consumer Price Index. The CPI measures the increase (or decrease) in the prices of goods and services relative to a base year. The CPI for the years 1990–2019 (using 1984 as a base period) is shown in the table below.

a. Graph the time series. Do you detect a long-term trend? Year CPI Year CPI 1990 125.8 2005 195.3 1991 129.1 2006 201.6 1992 132.8 2007 207.3 1993 136.8 2008 215.3 1994 147.8 2009 214.5 1995 152.4 2010 218.1 1996 156.9 2011 224.9 1997 160.5 2012 229.6 1998 163.0 2013 233.0 1999 166.6 2014 236.7 2000 171.5 2015 237.0 2001 177.1 2016 240.0 2002 179.9 2017 245.1 2003 184.0 2018 251.1 2004 188.9 2019 254.4

b. Calculate and plot the exponentially smoothed series for the CPI using a smoothing constant of w = .4. Use the exponentially smoothed values to forecast the CPI in 2020.

c. Use Holt’s forecasting model with trend to forecast the CPI in 2020. Use smoothing constants w = .4 and v = .5.