## Question

You have been tasked with describing the historical data and with developing preliminary forecasts for the 2014 based on the historical data from the first quarter of 2007 (quarter 1) through the last quarter of 2013 (quarter 28).

1. Create a time series plot of all the data. Identify and state the pattern or patterns you observe in the historical data for the number of quarterly sales revenue? Be as specific and complete as necessary.

2. If you observe seasonality in the time series plot of part 1, confirm this by creating a seasonal plot. What is the length of the seasonality (that is, how many periods are in the seasonality)?

3. Construct the graph of the autocorrelation function (ACF, as called the correlogram.

a. Attach a copy of your ACF to your submitted exam.

b. List the first 10 autocorrelation coefficients.

c. Are any of these coefficients significantly different from zero? If so, which ones and state why? (You may manually test each coefficient or use the ACF itself.)

d. On the basis of your ACF, is the data trended or not? Either way, state why.

e. On the basis of your ACF, is the data seasonal or not? Either way, state why.

4. Calculate and state the forecasts for as many quarters of 2014 as possible by the following five simple forecasting methods:

a. Simple naïve.

b. Simple moving averages with equal to the period of the seasonality (as you stated in part 2).

c. Simple exponential smoothing with a = 0.2 (initialize with F1 = y1).

d. Simple exponential smoothing with a = 0.7 (initialize with

e. Simple exponential smoothing with a optimized by Minitab.

5. a. Calculate and state the accuracy of each of the forecasting methods in part 4 using the root mean square error (RMSE) as the measure.

b. Which is the most accurate of these simple methods?

c. What are the most accurate forecasts?

6. Calculate and state the forecasts for as many quarters of 2014 as possible by the following five "advanced" forecasting methods:

a. Double moving averages with m equal to the period of the seasonality found in part 2.

Double exponential-smoothing with

c. Holt's method using Minitab's "Double Exponential Smoothing" tool with "Optimal ARIMA" button selected under "Weights to Use in Smoothing."

d. Winter's multiplicative method using Minitab's "Winter's method" tool with "Multiplicative" selected under "Method Type." Use the default settings for the weights for level, trend, and seasonal to use in smoothing.

e. Winter's additive method using Minitab's "Winter's method" tool with

"Additive" selected under "Method Type."

Remark: For parts c, d, and e, click "Generate forecasts" and for "Number of forecasts" enter the period of the seasonality that you stated in part 2.

7. a. Calculate and state the accuracy of each of the forecasting methods in part 6 using the RMSE as the measure. (Hint: The MSE is stated on the Minitab graphs as "MSD.")

b. Which is the most accurate of these advanced methods?

c. What are the most accurate forecasts?

8. Perform a time series regression (simple linear regression with time) of the historical data for its trend component. For the parts below, generate a regression output report produced in either Excel or Minitab and submit it with your completed test.

a. State the equation of the fitted regression line.

b. (1) State the numerical value of the coefficient of determination.

(2) State what this coefficient measures.

c. State the numerical value of the correlation coefficient. On this basis, how strongly (or not) does the sales revenue depend on time (by quarter).

d. On the basis of this regression analysis, calculate and state the sales revenue forecasts for all four quarters of 2014.

e. Calculate and state the RMSE of this simple linear regression. [

9. Perform the following time series decompositions in Minitab. (Go to Stat > Time Series > Decomposition; for all decompositions, set the seasonal length to what you stated in part 2.)

a. Additive with trend alone; state the sales revenue forecasts for all four quarters of 2014.

b. Additive with seasonal only; state the sales revenue forecasts for as many quarters of 2014 as possible.

c. Additive with trend plus seasonal; state the sales revenue forecasts for all four quarters of 2014.

d. Multiplicative with seasonal only; state the sales revenue forecasts for as many quarters of 2014 as possible.

d. Multiplicative with trend only; state the sales revenue forecasts for as many quarters of 2014 as possible.

e. Multiplicative with trend plus seasonal; state the sales revenue forecasts for all four quarters of 2014.

f. On the basis of the Minitab time series decomposition plots, do you recommend forecasting with the trend component alone (as you were asked to do in part 8.d above), the seasonal component alone, or both the trend and seasonal components together.

10. a. Calculate and state the accuracy of each of the forecasting methods in part 9 using the RMSE as the measure. (Note: MSE is stated on the Minitab graphs as "MSD." RMSE is the square root of this value.)

b. Which is the most accurate of these two time series decomposition methods?

c. What are the most accurate forecasts?

11. Of all the methods used in this case study (in parts 4 and 5, parts 6 and 7, part 8, and parts 9 and 10),

a. Which is the most accurate of these advanced methods?

b. What are the most accurate forecasts?

c. Submit the graph of this most accurate method showing the forecasts.

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