1. Calculate seasonal ratio for the passenger series y(t). The basic idea behind seasonal ratios can be seen by rearranging the trend-times-seasonal model:

yTREND =SEASON

For each of the estimated levels given by the centered moving averages, we calculate the ratio of actual sales divided by the centered moving average and enter = D4 / F4 in cell G4 and then copy the formula down to cell G20. This ratio tells us how to seasonally adjust a series.

Because we have more than one seasonal ratio observation for a given quarter, we average these ratios by quarter. That is, we compute the average for all the quarter 1 ratios, then the average for all the quarter 2 ratios, and so on. These averages become our seasonal ratio estimates.

Show the resulting ratios based on the periods of 1, 2, 3 and 4 in the table below:

Quarter	Seasonality ratio
1
2
3
4

(15p.)

Year	Quarter	t	y(t)
2009	1	1	110569
	2	2	113433
	3	3	118183
	4	4	114932
2010	1	5	112337
	2	6	117224
	3	7	118863
	4	8	116554
2011	1	9	116287
	2	10	124077
	3	11	126540
	4	12	123559
2012	1	13	122607.4
	2	14	129549.7
	3	15	128105.9
	4	16	126818.9
2013	1	17	123020.3
	2	18	130158.9
	3	19	133584.3
	4	20	132147.9
2014	1	21	126932.4

Time Series plot of quarterly light rail usage (first quarter 2009 through first quarter 2014) 140000 135000 130000 Passengers (thousands) 125000 120000 115000 110000 0 36 18 21 24 9 12 15 Time (quarters) Time Series plot of quarterly light rail usage (first quarter 2009 through first quarter 2014) 140000 135000 130000 Passengers (thousands) 125000 120000 115000 110000 0 36 18 21 24 9 12 15 Time (quarters)