Question

The following data show the number of issues from Initial Public Offerings (IPOs) from 2006 to 2019 released by the Security Data Company. Use these data to develop forecasts for the year.

YEAR

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

2018

2019

NUMBER OF ISSUES

133

169

151

122

120

127

136

151

166

157

157

186

160

190

(a) Calculate three years moving average forecasts for the year 2020. Also evaluate the quality of the forecast by calculating the root-mean-square error for the data set.

(b) Calculate exponential smoothing forecasts with w = 0.3 for the year 2020. Also evaluate the quality of the exponential smoothing model by calculating the root-mean-square error for the data set.

Answer 1

Simple moving average is simply the average of last 3 years given data.

		Simple Moving average
2007	169
2008	151
2009	122	151.00
2010	120	147.33
2011	127	131.00
2012	136	123.00
2013	151	127.67
2014	166	138.00
2015	157	151.00
2016	157	158.00
2017	186	160.00
2018	160	166.67
2019	190	167.67
2020		178.67

		Simple Moving average	Error	Squared error
2007	169
2008	151
2009	122	151.00	(29.00)	841.00
2010	120	147.33	(27.33)	747.11
2011	127	131.00	(4.00)	16.00
2012	136	123.00	13.00	169.00
2013	151	127.67	23.33	544.44
2014	166	138.00	28.00	784.00
2015	157	151.00	6.00	36.00
2016	157	158.00	(1.00)	1.00
2017	186	160.00	26.00	676.00
2018	160	166.67	(6.67)	44.44
2019	190	167.67	22.33	498.78
2020		178.67

Sum of squared error	4,357.78
Divide the sum by 11 (n)	396.16
Square root of above	19.90

RMSE is 19.9 which is not very high as compared to the given data mean i.e. close to 152

b)

The below exponential forecast is calculated using the weight of previous year as 0.7 and weight for one year before that as 0.3.

		Exponential
2007	169
2008	151	158.2
2009	122	156.4
2010	120	130.7
2011	127	120.6
2012	136	124.9
2013	151	133.3
2014	166	146.5
2015	157	161.5
2016	157	159.7
2017	186	157
2018	160	177.3
2019	190	167.8
2020		181

2006

133

		Exponential	Error	Squared error
2007	169
2008	151	158.2	-7.2	51.84
2009	122	156.4	-34.4	1183.36
2010	120	130.7	-10.7	114.49
2011	127	120.6	6.4	40.96
2012	136	124.9	11.1	123.21
2013	151	133.3	17.7	313.29
2014	166	146.5	19.5	380.25
2015	157	161.5	-4.5	20.25
2016	157	159.7	-2.7	7.29
2017	186	157	29	841
2018	160	177.3	-17.3	299.29
2019	190	167.8	22.2	492.84
2020		181

Sum of squared error	3868.07
Divide the sum by 12 (n)	322.34
Square root of above	17.95

RMSE is lesser in this model. 17.95 as compared to previous model. So this model is better than the previous one.