You are given the following quarterly sales information for ASTRA Company over the last 3 years.table attached (image) Find the centered moving averages (CMA). Construct the seasonal and irregular components of the data. ANOVASignificancedfSSMSFFRegression132.42641 32.42641172.32350.0000Residual101.881718 0.188172Total1134.30813StandardCoefficientsErrort Statp-valueLower 95%Upper 95%Intercept37.10340.2670 138.97540.000036.508537.6982T0.47620.036313.12720.00000.39540.5570 Four-periodmovingSalesRatio toSeasonalDeseasonalizedТabunQuarterСМАСМАIndex(Rp Billion)averageSales2016138201623738.5201633938.9201644039.12017139.439.420173839.82017340.240.22017441.440.9201814141.62018240.842.320183432018444.4

Answered: You are given the following quarterly…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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You are given the following quarterly sales information for ASTRA Company over the last 3 years.

table attached (image)

Find the centered moving averages (CMA).
Construct the seasonal and irregular components of the data.

ANOVA
Significance
df
SS
MS
F
F
Regression
1
32.42641 32.42641
172.3235
0.0000
Residual
10
1.881718 0.188172
Total
11
34.30813
Standard
Coefficients
Error
t Stat
p-value
Lower 95%
Upper 95%
Intercept
37.1034
0.2670 138.9754
0.0000
36.5085
37.6982
T
0.4762
0.0363
13.1272
0.0000
0.3954
0.5570

Four-period
moving
Sales
Ratio to
Seasonal
Deseasonalized
Тabun
Quarter
СМА
СМА
Index
(Rp Billion)
average
Sales
2016
1
38
2016
2
37
38.5
2016
3
39
38.9
2016
4
40
39.1
2017
1
39.4
39.4
2017
38
39.8
2017
3
40.2
40.2
2017
4
41.4
40.9
2018
1
41
41.6
2018
2
40.8
42.3
2018
3
43
2018
4
44.4

Expert Solution

Step 1

1. Centered moving average

To compute the central moving average, take the average to two consecutive moving averages.

[example : average of $38.5 a n d 38.9$ , the average of $38.9 a n d 39.1$ and so on]

Now, to compute ratio to moving average, express the original values as the percentage of the centered moving average.

[example : $(39 / 38.7) \times 100 = 100.78$ ]

These percentages represents the seasonal and irregular components using the multiplicative model.

$\begin{array}{rcl} y_{t} & = & T_{t} \times S_{t} \times C_{t} \times I_{t} \\ \frac{y_{t}}{T_{t} \times C_{t}} & = & S_{t} \times I_{t} \end{array}$

[Note : The moving average values contains the estimated combination of trend and cyclic component]

Tahun	Quarter	Sales	Four-Period Moving Average	CMA	Ratio to CMA
2016	1	38

2016	2	37
			38.5
2016	3	39		38.7	100.78
			38.9
2016	4	40		39	102.56
			39.1
2017	1	39.4		39.25	100.38
			39.4
2017	2	38		39.6	95.96
			39.8
2017	3	40.2		40	100.50
			40.2
2017	4	41.4		40.6	101.97
			40.9
2018	1	41		41.25	99.39
			41.6
2018	2	40.8		41.95	97.26
			42.3
2018	3	43

2018	4	44.4

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