Consider the data on Walmart sales available in Walmart_2.xlsx Download Walmart_2.xlsx. Plot the quarterly sales data and verify that the series exhibits a seasonal element. Using the ESM contrast the additive seasonal, multiplicative seasonal, and logarithmic forms for forecasting sales, using the last 12 quarters as a hold-out sample.

Year	Walmart Stores	Super Stores	Sam's Club		Year	Quarter	Sales ($ billion)
1995	2176	154	453		2003	1	56.7
1996	2218	255	470		2003	2	62.6
1997	1960	344	436		2003	3	62.5
1998	1921	441	443		2003	4	74.5
1999	1860	564	451		2004	1	64.8
2000	1801	721	463		2004	2	69.7
2001	1736	888	475		2004	3	68.5
2002	1647	1066	500		2004	4	82.2
2003	1568	1258	525		2005	1	70.0
2004	1478	1471	538		2005	2	75.9
2005	1353	1713	551		2005	3	74.6
2006	1209	1980	567		2005	4	88.4
2007	1075	2256	579		2006	1	78.8
2008	971	2447	591		2006	2	84.5
2009	891	2612	602		2006	3	83.5
2010	708	2907	609		2006	4	98.1
2011	629	3029	611		2007	1	85.4
2012	561	3158	620		2007	2	92.0
2013	508	3288	632		2007	3	90.9
2014	470	3407	647		2007	4	106.3
2015	442	3465	655		2008	1	94.1
					2008	2	101.6
					2008	3	97.6
					2008	4	108.0
					2009	1	93.5
					2009	2	100.1
					2009	3	98.7
					2009	4	112.8
					2010	1	99.1
					2010	2	103
					2010	3	101.2
					2010	4	115.6
					2011	1	103.4
					2011	2	108.6
					2011	3	109.5
					2011	4	122.3
					2012	1	112.3
					2012	2	113.5
					2012	3	113.2
					2012	4	127.1
					2013	1	113.3
					2013	2	116.1
					2013	3	114.9
					2013	4	128.8
					2014	1	114.2
					2014	2	119.3
					2014	3	118.1
					2014	4	130.7
					2015	1	114
					2015	2	119.3
					2015	3	116.6
					2015	4	128.7

Year	Quarter	Sales ($ billion)	GDP	L1_GDP	L4_GDP	L1_Sales	L4_Sales
2003	1	56.7	11230.1
2003	2	62.6	11370.7	11230.1		56.7
2003	3	62.5	11625.1	11370.7		62.6
2003	4	74.5	11816.8	11625.1		62.5
2004	1	64.8	11988.4	11816.8	11230.1	74.5	56.7
2004	2	69.7	12181.4	11988.4	11370.7	64.8	62.6
2004	3	68.5	12367.7	12181.4	11625.1	69.7	62.5
2004	4	82.2	12562.2	12367.7	11816.8	68.5	74.5
2005	1	70.0	12813.7	12562.2	11988.4	82.2	64.8
2005	2	75.9	12974.1	12813.7	12181.4	70.0	69.7
2005	3	74.6	13205.4	12974.1	12367.7	75.9	68.5
2005	4	88.4	13381.6	13205.4	12562.2	74.6	82.2
2006	1	78.8	13648.9	13381.6	12813.7	88.4	70.0
2006	2	84.5	13799.8	13648.9	12974.1	78.8	75.9
2006	3	83.5	13908.5	13799.8	13205.4	84.5	74.6
2006	4	98.1	14066.4	13908.5	13381.6	83.5	88.4
2007	1	85.4	14233.2	14066.4	13648.9	98.1	78.8
2007	2	92.0	14422.3	14233.2	13799.8	85.4	84.5
2007	3	90.9	14569.7	14422.3	13908.5	92.0	83.5
2007	4	106.3	14685.3	14569.7	14066.4	90.9	98.1
2008	1	94.1	14668.4	14685.3	14233.2	106.3	85.4
2008	2	101.6	14813.0	14668.4	14422.3	94.1	92.0
2008	3	97.6	14843.0	14813.0	14569.7	101.6	90.9
2008	4	108.0	14549.9	14843.0	14685.3	97.6	106.3
2009	1	93.5	14383.9	14549.9	14668.4	108.0	94.1
2009	2	100.1	14340.4	14383.9	14813.0	93.5	101.6
2009	3	98.7	14384.1	14340.4	14843.0	100.1	97.6
2009	4	112.8	14566.5	14384.1	14549.9	98.7	108.0
2010	1	99.1	14681.1	14566.5	14383.9	112.8	93.5
2010	2	103	14888.6	14681.1	14340.4	99.1	100.1
2010	3	101.2	15057.7	14888.6	14384.1	103.0	98.7
2010	4	115.6	15230.2	15057.7	14566.5	101.2	112.8
2011	1	103.4	15238.4	15230.2	14681.1	115.6	99.1
2011	2	108.6	15460.9	15238.4	14888.6	103.4	103.0
2011	3	109.5	15587.1	15460.9	15057.7	108.6	101.2
2011	4	122.3	15785.3	15587.1	15230.2	109.5	115.6
2012	1	112.3	15973.9	15785.3	15238.4	122.3	103.4
2012	2	113.5	16121.9	15973.9	15460.9	112.3	108.6
2012	3	113.2	16227.9	16121.9	15587.1	113.5	109.5
2012	4	127.1	16297.3	16227.9	15785.3	113.2	122.3
2013	1	113.3	16475.4	16297.3	15973.9	127.1	112.3
2013	2	116.1	16541.4	16475.4	16121.9	113.3	113.5
2013	3	114.9	16749.3	16541.4	16227.9	116.1	113.2
2013	4	128.8	16999.9	16749.3	16297.3	114.9	127.1
2014	1	114.2	17025.2	16999.9	16475.4	128.8	113.3
2014	2	119.3	17285.6	17025.2	16541.4	114.2	116.1
2014	3	118.1	17569.4	17285.6	16749.3	119.3	114.9