Question

tables 1-5 please compute the exponentially smoothed forecast using an α=0.1; the reaminder of the tables please use the α =0.9

- computer student loan debt usign each model for 2016?

- which method is the best forecasting method?

- why does the moving average lag the demand?

period	actual	naive	3 month moving average	exponentially smoothed forecast	naive error	MA error	Exp. Error
2006	500.01			F1=495
2007	565.28
2008	644.91
2009	733.48
2010	828.31
2011	926.88
2012	1026.41
2013	1118.70
2014	1209.25
2015	1295.52

Answer 1

period	actual	naive	3 month moving average	exponentially smoothed forecast	naive error	MA error	Exp. Error
2006	500.01			495.00
2007	565.28	500.01		499.51	65.27		65.77
2008	644.91	565.28		558.70	79.63		86.21
2009	733.48	644.91	570.07	636.29	88.57	163.41	97.19
2010	828.31	733.48	647.89	723.76	94.83	180.42	104.55
2011	926.88	828.31	735.57	817.86	98.57	191.31	109.02
2012	1026.41	926.88	829.56	915.98	99.53	196.85	110.43
2013	1118.70	1026.41	927.20	1015.37	92.29	191.50	103.33
2014	1209.25	1118.70	1024.00	1108.37	90.55	185.25	100.88
2015	1295.52	1209.25	1118.12	1199.16	86.27	177.40	96.36

In naive we just place the last actual demand as the forecast for next year. forecast for 2007 is actual demand of 2006 od 500.01

In moving average, we add last 3 actual demands and divide by three to take an average. This is 3 year moving average. forecast for 2009 = (500.01+565.28+644.91)/3 = 570.07

exponential smoothing = f*a + s*(1-a)

a = 0.1 = alpha

f = forecast for previous year

s = actual demand for previous year

forecast for 2007 = 495*0.1 + 500.01*0.9 = 499.51

b) total error for naive = 795.51

total error for 3 year moving average = 1286.15

total error for exponential smoothing = 873.75

looking at the error, naive has least error. Hence for this situation naive is giving best results. In general exponential is a good method for forecast.

c) since the demand is rising each year the 3 year moving average is providing a low forecast due to averaging. This is because the 3-year moving average is lagging behind a lot.