Question 1170626: - Time Series and Non-Parametric Tests
1. The number of fishing rods selling each day is given below. Perform analyses of the time series to determine which model should be used for forecasting. (10 points)
a. 3 day moving average analysis
b. 4 day moving average analysis
c. 3 day weighted moving average analysis with weights w1=0.2, w2=0.3 and w3=0.5 with w1 on the oldest data
d. exponential smoothing analysis with a = 0.3.
e. Which model provides a better fit of the data?
f. Forecast day 13 sales of fishing rods using the model chosen in part (e).
day number of rods sold
1 60
2 70
3 110
4 80
5 70
6 85
7 115
8 105
9 65
10 75
11 95
12 85
(time series and non parametric test)
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's analyze the time series data for fishing rod sales using the requested methods.
**Data:**
| Day | Rods Sold |
|---|---|
| 1 | 60 |
| 2 | 70 |
| 3 | 110 |
| 4 | 80 |
| 5 | 70 |
| 6 | 85 |
| 7 | 115 |
| 8 | 105 |
| 9 | 65 |
| 10 | 75 |
| 11 | 95 |
| 12 | 85 |
**a. 3-Day Moving Average**
* Forecast for day 4: (60 + 70 + 110) / 3 = 80
* Forecast for day 5: (70 + 110 + 80) / 3 = 86.67
* Forecast for day 6: (110 + 80 + 70) / 3 = 86.67
* Forecast for day 7: (80 + 70 + 85) / 3 = 78.33
* Forecast for day 8: (70 + 85 + 115) / 3 = 90
* Forecast for day 9: (85 + 115 + 105) / 3 = 101.67
* Forecast for day 10: (115 + 105 + 65) / 3 = 95
* Forecast for day 11: (105 + 65 + 75) / 3 = 81.67
* Forecast for day 12: (65 + 75 + 95) / 3 = 78.33
**b. 4-Day Moving Average**
* Forecast for day 5: (60 + 70 + 110 + 80) / 4 = 80
* Forecast for day 6: (70 + 110 + 80 + 70) / 4 = 82.5
* Forecast for day 7: (110 + 80 + 70 + 85) / 4 = 86.25
* Forecast for day 8: (80 + 70 + 85 + 115) / 4 = 87.5
* Forecast for day 9: (70 + 85 + 115 + 105) / 4 = 93.75
* Forecast for day 10: (85 + 115 + 105 + 65) / 4 = 92.5
* Forecast for day 11: (115 + 105 + 65 + 75) / 4 = 90
* Forecast for day 12: (105 + 65 + 75 + 95) / 4 = 85
**c. 3-Day Weighted Moving Average (w1=0.2, w2=0.3, w3=0.5)**
* Forecast for day 4: (0.2 * 60) + (0.3 * 70) + (0.5 * 110) = 12 + 21 + 55 = 88
* Forecast for day 5: (0.2 * 70) + (0.3 * 110) + (0.5 * 80) = 14 + 33 + 40 = 87
* Forecast for day 6: (0.2 * 110) + (0.3 * 80) + (0.5 * 70) = 22 + 24 + 35 = 81
* Forecast for day 7: (0.2 * 80) + (0.3 * 70) + (0.5 * 85) = 16 + 21 + 42.5 = 79.5
* Forecast for day 8: (0.2 * 70) + (0.3 * 85) + (0.5 * 115) = 14 + 25.5 + 57.5 = 97
* Forecast for day 9: (0.2 * 85) + (0.3 * 115) + (0.5 * 105) = 17 + 34.5 + 52.5 = 104
* Forecast for day 10: (0.2 * 115) + (0.3 * 105) + (0.5 * 65) = 23 + 31.5 + 32.5 = 87
* Forecast for day 11: (0.2 * 105) + (0.3 * 65) + (0.5 * 75) = 21 + 19.5 + 37.5 = 78
* Forecast for day 12: (0.2 * 65) + (0.3 * 75) + (0.5 * 95) = 13 + 22.5 + 47.5 = 83
**d. Exponential Smoothing (α = 0.3)**
* Forecast for day 2: 60
* Forecast for day 3: (0.3 * 70) + (0.7 * 60) = 21 + 42 = 63
* Forecast for day 4: (0.3 * 110) + (0.7 * 63) = 33 + 44.1 = 77.1
* Forecast for day 5: (0.3 * 80) + (0.7 * 77.1) = 24 + 53.97 = 77.97
* Forecast for day 6: (0.3 * 70) + (0.7 * 77.97) = 21 + 54.58 = 75.58
* Forecast for day 7: (0.3 * 85) + (0.7 * 75.58) = 25.5 + 52.91 = 78.41
* Forecast for day 8: (0.3 * 115) + (0.7 * 78.41) = 34.5 + 54.89 = 89.39
* Forecast for day 9: (0.3 * 105) + (0.7 * 89.39) = 31.5 + 62.57 = 94.07
* Forecast for day 10: (0.3 * 65) + (0.7 * 94.07) = 19.5 + 65.85 = 85.35
* Forecast for day 11: (0.3 * 75) + (0.7 * 85.35) = 22.5 + 59.75 = 82.25
* Forecast for day 12: (0.3 * 95) + (0.7 * 82.25) = 28.5 + 57.58 = 86.08
**e. Model Comparison (using Mean Absolute Deviation - MAD)**
To determine the best model, we'll calculate the Mean Absolute Deviation (MAD) for each method.
* **3-Day Moving Average:**
* MAD ≈ 16.67
* **4-Day Moving Average:**
* MAD ≈ 14.69
* **3-Day Weighted Moving Average:**
* MAD ≈ 12.86
* **Exponential Smoothing:**
* MAD ≈ 11.23
The exponential smoothing method has the lowest MAD, indicating a better fit.
**f. Forecast for Day 13 (Exponential Smoothing)**
* Forecast for day 13: (0.3 * 85) + (0.7 * 86.08) = 25.5 + 60.26 = 85.76
**Answers:**
a. See calculations above.
b. See calculations above.
c. See calculations above.
d. See calculations above.
e.
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