Question

1. Smoothing methods (conceptual) Aa Aa Monthly time series data on coin collections from about 70,000 New York City parking meters between November 1979 and March 1981 are shown on the following graph. (Source: Michael O. Finkelstein and Bruce Levin, Statistics for Social Sciences and Public Policy: Statistics for Lawyers, second edition, Springer, 2001.) In addition to the time series, two forecasts of parking meter collections are shown on the graph, a three-month moving average and a five-month moving average. 2.0 1.9 1.8 Meter Collections ($ millions) 1.7 1.6 T Nov Jan Mar May Jul Sep Nov Mar Jan 1981 1979 1980 The blue (square symbol) line is the time series three-month moving average five-month moving average - men are shown again on the following graph. The monthly time series data on New

Answer 1

Moving averages are used to smooth out the trend of the time series data.

The bigger the window we take for the moving averages, the smoother our time series becomes.

(a) The blue ( square symbol) line is the " Three month moving average"

(b) The pink ( diamond symbol ) line is the " weighted moving average forecast"

(c) We see in the below graph that the lower the value of alpha, the smoother the curve and the higher the alpha the more trend is present or the more it resembles the actual time series.

Exponential Smoothing 1200 1000 800 Actual Price 600 Alpha=0.1 400 Alpha=0.3 Alpha=0.8 200 0 0 1 2 3 4 5 8 9 10 11 12 6 7 Period

Hence, The pink ( diamond symbol ) line is the "forecast that uses 0.2 smoothing parameter"