Answered: Passengers (thousands) 150000 145000…

Survey of Accounting (Accounting I)

8th Edition

ISBN:9781305961883

Author:Carl Warren

Publisher:Carl Warren

Chapter13: Budgeting And Standard Costs

Section: Chapter Questions

Problem 13.6.2MBA

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Related questions

Question

Figure 1 below displays the quarterly number of U.S. passengers (in thousands) using light rail as a mode of transportation. The series begins in the first quarter of 2015 and ends with the third quarter of 2024.

We can see a regularity to the series: the first quarter’s ridership tends to be lowest; then there is a progressive rise in ridership going into the second and third quarters, followed by a decline in the fourth quarter. Superimposed on the series are the moving-average forecasts based on a span of k = 4.

Notice that the seasonal pattern in the time series is not present in the moving averages. The moving averages are a smoothed-out version of the original time series, reflecting only the general trend in the series, which is upward.

Data Analysis Questions:

1. Calculate the centered moving average (CMA) that will be centered on t = 3.

This value can be seen in the spreadsheet below. Show the centered moving averages plotted on the passenger series y(t) and compare and interpret the trend of two series. Do not forget to label x and y axes and adjust the values on the plot using Figure 1.

Show your plot space provided below:

Now you have an appropriate baseline estimate for the level of the process historically, so you can compute the seasonal component. This seasonal ratio says that we can isolate the seasonal component by dividing the data by the level of series as estimated by the trend component.

Passengers (thousands)
150000
145000
140000
135000
130000
125000
120000
115000
110000
Time Series plot of quarterly light rail usage
(first quarter 2015 through third quarter 2024)
wwww
0
8
12
16
20
Time (Quarters)
24
28
32
36
40
40

Year
Quarter
t
y(t)
2015
1
1
110569
2
2
113433
3
3
118183
4
4
114932
2016
1
5
112337
2
6
117224
3
7
118863
4
8
116554
2017
1
9
116287
2
10
124077
3
11
126540
4
12
123559
2018
1
13
122607.4
2
14
129549.7
3
15
128105.9
4
16 126818.9
2019
1
17
123020.3
2
18
130158.9
3
19 133584.3
4
20
132147.9
2020
1
21 126932.4
2
22 123051.92]
3
23 134041.56
4
24 135031.20
2021
1
25 130020.840
2
26 128010.480
3
27 138000.12
4
28 139989.76
2022
1
29 140979.40!
2
30 135969.04
3
31 130958.68!
4
32 142948.32!
2023
1
33 144321.12!
2
34 139782.059
3
35 135372.74
4
36 147611.86
2024
123
37 149334.83
38 145124.004
39 141022.359

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