Question

Group Exercise #7

The tourist industry is subject to enormous seasonal variation.   A hotel in Bermuda has recorded its occupancy rate for each quarter over a 5-year period.    These data are shown in the following table:

Year	Quarter	Occupancy Rate
1995	1	0.561
	2	0.702
	3	0.800
	4	0.568
1996	1	0.575
	2	0.738
	3	0.868
	4	0.605
1997	1	0.594
	2	0.738
	3	0.729
	4	0.600
1998	1	0.622
	2	0.708
	3	0.806
	4	0.632
1999	1	0.665
	2	0.835
	3	0.873
	4	0.670

1. Calculate the seasonal indices for each quarter in order to measure seasonal variation.     Also, include the Trend Line Equation. (Hint:   Because the regression line yt = β0 + β1t    represents trend, it follows that the time series divided by the predicted values produces ytyt = S_t X R_tà seasonal & random variation.   And, because there is no cyclical effect, use this method to compute seasonal indices.)

2. What can you infer from the Seasonal Indices?

3. Deseasonalize the occupancy rates and assess.   (Hint:   Graphically compare the original and adjusted data sets.   Accordingly, provide data-supported inference/s.)

4. Forecast each quarter’s occupancy rate for 2000.

5. As an alternative to calculating and using seasonal indices to measure seasonal variations, indicator variables can be used in a multiple regression model.   Accordingly, use indicator variables and regression analysis to forecast hotel occupancy in 2000.   How does this compare to the forecast produced by using seasonal indices?  

Answer 1

The deseasonalized data and seasonal indexes are:

				Centered
				Moving	Ratio to	Seasonal	Occupancy Rate
t	Year	Quarter	Occupancy Rate	Average	CMA	Indexes	Deseasonalized
1	1	1	0.561			0.881	0.6365
2	1	2	0.702			1.075	0.6532
3	1	3	0.800	0.660	1.213	1.173	0.6822
4	1	4	0.568	0.666	0.853	0.871	0.6519
5	2	1	0.575	0.679	0.847	0.881	0.6524
6	2	2	0.738	0.692	1.067	1.075	0.6867
7	2	3	0.868	0.699	1.242	1.173	0.7402
8	2	4	0.605	0.701	0.863	0.871	0.6944
9	3	1	0.594	0.684	0.869	0.881	0.6740
10	3	2	0.738	0.666	1.108	1.075	0.6867
11	3	3	0.729	0.669	1.090	1.173	0.6217
12	3	4	0.600	0.669	0.898	0.871	0.6886
13	4	1	0.622	0.674	0.922	0.881	0.7057
14	4	2	0.708	0.688	1.029	1.075	0.6588
15	4	3	0.806	0.697	1.156	1.173	0.6874
16	4	4	0.632	0.719	0.879	0.871	0.7254
17	5	1	0.665	0.743	0.895	0.881	0.7545
18	5	2	0.835	0.756	1.104	1.075	0.7769
19	5	3	0.873			1.173	0.7445
20	5	4	0.670			0.871	0.7690
	Calculation of Seasonal Indexes
	1	2	3	4
1			1.213	0.853
2	0.847	1.067	1.242	0.863
3	0.869	1.108	1.090	0.898
4	0.922	1.029	1.156	0.879
5	0.895	1.104
mean:	0.883	1.077	1.175	0.873	4.009
adjusted:	0.881	1.075	1.173	0.871	4.000

The trend line equation is:

y = 0.0053x + 0.6385

The plotted data is: