Question

Year	Qtr	t	revenue ($M)
2011	1	1	5.889
	2	2	6.141
	3	3	8.272
	4	4	9.302
2012	1	5	6.436
	2	6	6.932
	3	7	8.987
	4	8	10.602
2013	1	9	7.517
	2	10	7.731
	3	11	9.883
	4	12	12.098
2014	1	13	8.487
	2	14	8.685
	3	15	11.559
	4	16	15.221
2015	1	17	11.132
	2	18	11.203
	3	19	13.83
	4	20	16.979
2016	1	21	12.312
	2	22	13.452
	3	23	17.659
	4	24	21.655
2017	1	25	17.197
	2	26	19.05
	3	27	22.499
	4	28	25.629

Which is the most accurate method of the decomposition methods used for the following data set.
Additive with seasonal only, Additive with trend plus seasonal , Multiplicative with seasonal only ,Multiplicative with trend plus seasonal

Answer 1

A given data is said to be seasonal only if the values change according to the season but do not vary with time. In other words for a given data set, the values can change within the year but they shouldn't change from year to year.

A given data is said to be trend plus seasonal if the values change according to the season and also show a trend with time. In other words for a given data set, the values are dependent on the season(or quarter of the year) and also with time the values are seen to be changing ....something like the values for a year are 1+ values of the year before.

Now a trend can be either additive or multiplicative, it is said to be additive if after every year the values are being added by a specific value (this means the difference between 2 quarters is constant). It is said to be multiplicative if after every year the vaues are being scaled by a specific value (this means the difference between 2 quarter also changes with year)

Now coming to our dataset, on observing that there are differences from year to year we can certainly say that it is not seasonal only, but we do see the revenue to change according to which quarter they are in, therefore it has seasonal properties and we observe that it is has a trend as well, because it is increasing through the years. So we can say that it is trend plus seasonal. Now we have the task of finding out whether the trend is additive or multiplicative.

We do a simple observation to solve this problem, we compare the difference of revenues of 1st quarter and last quarter, this difference starts from around $4M and slowly goes up until around $9M(i.e not constant). Implying that the trend is multiplicative.

The most accurate method of decomposition methods used for the following data set is Multiplicative with trend plus seasonal.

(PS: It will be easier to understand and decide these properties by converting the table into a graph.)