S&P 500 Stock Index. Standard & Poor’s 500 Composite Stock Index (S&P 500) is a stock market index. Like the Dow Jones Industrial Average, it is an indicator of stock market activity. The data in the table are end-of-quarter values of the S&P 500 for the years 2012–2019.

a. Calculate and plot the exponentially smoothed series for the quarterly S&P 500 using a smoothing constant of w = .3.

b. Repeat part a but use w = .7.

c. Which exponentially smoothed series do you prefer for describing trends in the series? Explain. Year Quarter S&P 500 Year Quarter S&P 500 2012 1 1348.8 2016 1 2059.7 2012 2 1349.7 2016 2 2098.9 2012 3 1400.9 2016 3 2168.3 2012 4 1418.1 2016 4 2238.8 2013 1 1514 2017 1 2362.7 2013 2 1609.5 2017 2 2423.4 2013 3 1674.9 2017 3 2519.4 2013 4 1768.7 2017 4 2673.6 2014 1 1834.9 2018 1 2640.9 2014 2 1900.4 2018 2 2718.4 2014 3 1975.9 2018 3 2914.0 2014 4 2009.3 2018 4 2506.9 2015 1 2067.9 2019 1 2834.4 2015 2 2063.1 2019 2 2941.8 2015 3 1920.0 2019 3 2976.7 2015 4 2043.9 2019 4 3230.8 Source: FRED, Economic Research, Federal Reserve Bank of St. Louis (fred.stlouisfred.org)