Question 4: The smoothing constant chosen in simple exponential smoothing determines the
weight to be placed on different terms of time-series data. If the smoothing factor is high
rather than low, is more or less weigh placed on recent observations? If a is .3, what weight is
applied to the observation four periods ago?
- When the smoothing factor is high, more weight is placed on past observations, and
less weight is placed on recent observations
- .07203
Question 6: The following inventory pattern has been observed in the Zahm Corporation over
12 months. Use both three-month and five-month moving-average models to forecast the
inventory for the next January. Use mean absolute percentage error (MAPE) to evaluate
these two forecasts.
- 3 month for next January is 1,925.33
- 5 month for next January is 1,848
- When looking at both forecasts, the MAPE for the 3 month is 22.69, and the MAPE
for the 5 month is 23.79. Therefore the 3 month moving-average is better at
forecasting because it has a lower MAPE.
Question 11: a. Plot the data presented in Exercise 7 to examine the possible existence of
trend and seasonality in the data.
- There is a strong positive trend in the data
b. Prepare three separate exponential smoothing models to forecast the full-service
restaurant sales data using the monthly data.
1. A simple smoothing model
2. Holt’s model
3. Winters’ model
c. Examine the accuracy of each model by calculating the mean absolute percentage
error for each during the historical period. Explain carefully what characteristics of the
original data led one of these models to have the lowest MAPE.
- Simple exponential smoothing MAPE= 536.011
-Holts model MAPE= 598.59
-Winters model MAPE= 253.204
-Overall Winters’ model had the lowest MAPE of 253.204, and the main factor that led
to it being so low was seasonality.
Question 12: The data in the table below represent warehouse club and superstore sales in
the eastern and central United States on a monthly basis. The data are in millions of dollars.
a. Prepare a time-series plot of the data, and visually inspect that plot to determine
the characteristics you see in this series.
- There is seasonality in the plot
- There is a positive trend
b. Use an exponential smoothing model to develop a forecast of sales for the next 12
months, and explain why you selected that model. Plot the actual and forecast
values. Determine the MAPE for your model during the historical period.
- I chose to use Winters’ exponential smoothing model because it works well to show
seasonality.
- MAPE= 348.1
Question 13: The data in the table below are for retail sales in book stores by quarter.
a. Plot these data and examine the plot. Does this view of the data suggest a
particular smoothing model? Do the data appear to be seasonal? Explain
- Yes, the data appears to be seasonal with June falling on the low end and December
and March on the high end.
- The Holt Winters’ Model would be the best to use
b. Use and exponential smoothing method to forecast the next four quarters. Plot
the actual and forecast values.
Question 16: How are simple moving averages models different from exponential smoothing
models?
-Simple moving average models are different in that they use simple averages whereas
exponential smoothing models use weighted averages of the data. Simple moving average
calculates the average of price data and exponential calculates the weight.
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