South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York. The following data show quarterly sales revenues (in $’000s) for the past 5 years.

Quarter | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |

1 | 20 | 37 | 75 | 92 | 176 |

2 | 100 | 136 | 155 | 202 | 282 |

3 | 175 | 245 | 326 | 384 | 445 |

4 | 13 | 26 | 48 | 82 | 181 |

**Question 1 (5 pts)**

Plot this data with quarters from years 1-5 on the horizontal axis. What components do you see in this time series?

**Question 2 (20 pts)**

Ignore any trend or seasonality in the data.

- Suppose the company uses moving averages to make forecasts.Make forecasts all the way through Q4 Year 5.Assume the company uses (i) 3-quarterly moving averages and (ii) 4-quarterly moving averages.
- Compare the two sets of forecasts from (a) on the basis of Mean Absolute Percent Deviation.Which is more accurate – 3 quarterly moving average or 4 quarterly moving average?
- On a line chart plot the time series along with the forecasts from the method you select in (b).

**Question 3 (20 pts)**

Ignore any trend or seasonality in the data.

- Suppose the company uses weighted moving averages to make forecasts.Make forecasts all the way through Q4 Year 5.Assume the company uses (i) 3-quarterly moving averages with weights 0.6, 0.3, and 0.1 and (ii) 4-quarterly moving averages with weights 0.4, 0.3, 0.2, and 0.1.In both cases the most weight is given to the most recent quarter and the least to the oldest quarter in the moving average.
- Compare the two sets of forecasts from (a) on the basis of Mean Absolute Percent Deviation.Which is more accurate – 3 quarterly weighted moving average or 4 quarterly weighted moving average?
- On a line chart plot the time series along with the forecasts from the method you select in (b).

**Question 4 (20 pts)**

Again ignore any trend or seasonality in the data.

- Suppose the company uses exponential smoothing to make forecasts.What are the forecasts for periods Q2 Year 1 through Q4 Year 5 assuming (i) alpha = 0.3 and (ii) alpha = 0.7?In both cases assume that the forecast for Q1 Year 1 was 25 units.
- Compare the two sets of forecasts from (a) on the basis of Mean Absolute Percent Deviation.Which is more accurate – alpha of 0.3 or alpha of 0.7?
- On a line chart plot the time series along with the forecasts from the method you select in (b)

**Question 5 (20 pts)**

Now make adjustments for trend and seasonality.

- Quantify the trend in the time series.What does the trend equation tell you?
- Quantify the seasonality in the time series by calculating seasonality indexes.What do these indexes tell you?
- Using the trend and the seasonality information from (a) and (b) make forecasts from Q1 Year 1 through Q4 Year 5.
- Calculate the Mean Absolute Percent Deviation for the forecasts in (c).
- On a line chart plot the time series along with the forecasts from (c).

**Question 6 (15 pts)**

Using the most accurate method of all of the above,

- Make forecasts for the four quarters of Year 6.
- Plot these forecasts on the same line chart as the time series.
- Summarize in a few lines your findings from your answers to Q1 through Q6b.