****THIS REQUIRES STATTOOLS (I've attached a .zip file containing the program)*** **

**QM203 - HW ASSIGNMENTS (AWZ 4 ^{th} ed)**

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**HW Set #4 - Ch 12 – Time Series Analysis and Forecasting (Read All)**

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** **09 (refers to P12_01) Linear trend (airline tickets), forecast error, seasonal?

Question 9: The file P12_01.xlsx contains the monthly number of airline tickets sold by a travel agency.

a. Does a linear trend appear to fit these data well? If so, estimate and interpret the linear trend model for this time series. Also, interpret *R2* and *se* values.

b. Provide an indication of the typical forecast error generated by the estimated model in part a.

c. Is there evidence of some seasonal pattern in these sales data? If so, characterize the seasonal pattern.

11 (refers to P12_11) National debt; exponential trend, predict

Question 11: The file P12_11.xlsx contains monthly values of the US National Debt (in dollars) from 1993 to early 2010. Fit an exponential growth curve to these data. Write a short report to summarize your findings. If the US national debt continues to rise at the exponential rate you find, approximately what will its value be at the end of 2020?

27 (refers to P02_44) Autoregressive (% children below poverty level)

Question 27: Consider the proportion of Americans under the age of 18 living below the poverty level. The data area in the file P02_44.xlsx.

a. Find the first six autocorrelations of this time series.

b. Use the results of part **a** to specify one or more promising autoregression models. Estimate each model with the available data. Which model provides the best fit to the data?

c. Use the best autoregression model from part **b** to produce a forecast of the proportion of American children living below the poverty level in the next year. Also, provide a measure of the likely forecast error.

30 (refers to P02_21) Autoregressive (mortgage rate)

Question 30: Consider the average annual interest rates on 30-year fixed mortgages in the United States. The data are recoded in the file P02_21.xslx.

a. Specify one or more promising autoregression models based on autocorrelations of this time series. Estimate each model with the available data. Which model provides the nest fit to the data?

b. Use the best autoregression model from part **a** to produce forecasts of the average annual interest rates on 30 year fixed mortgages in the next three years.

35 (refers to P12_16) Moving average (AmEx closing prices)

Question 35: The file P12_16.xslx contains the daily closing prices of American Express stock for a one year period.

a. Using a span of 3, forecast the price of this stock for the next trading day with the moving average method. How well does this method with span 3 forecast the known observations of this series?

b. Repeat part **a **with a span of 10

c. Which of these two spans appears to be more appropriate? Justify your answer.

37 (refers to P12_19) Moving average (AmEx closing prices); which span?

Question 37: The closing value of the Dow Jones Industrial Average for each trading day during a one yea period is provided in the fine P12_19.xslx.

a. Using a span of 2, forecast the price of this index on the next trading day with the moving average method. How well does the moving average method with span 2 forecast the known observations in this series?

b. Repeat part **a **with a span of 5; with a span of 15.

c. Which of these three spans appears to be most appropriate? Justify your choice.

42 (refers to P12_01) Exponential smoothing (airline tickets)

Question 42: Consider the airline ticket data in the file P12_01.xslx.

a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think should be used for forecasting? Why?

b. Use simple exponential smoothing to forecast these data, using no holdout period and requesting 12 months of future forecasts. Use the default smoothing constant of 0.1.

c. Repeat part **b** optimizing the smoothing constant.

d. Write a short report to summarize your results.

45 (refers to P02_44) Exponential smoothing (poverty level)

Question 45: Consider the poverty level data in the file P02_44.xslx.

a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think should be used for forecasting? Why?

b. Use simples exponential smoothing to forecast these data, using no holdout period and requesting three years of future forecasts. Use the default smoothing constant of 0.1.

c. Repeat part **b** optimizing the smoothing constant. Make sure you request a chart of the series with the forecasts superimposed. Does the Optimize Parameters option make much of an improvement?

d. Write a short report to summarize your results. Considering the chart in part **c** would you say the forecasts are adequate?

54 (refers to P02_55) Ratio-to-moving-average (MA, Holt) (beer/wine/liquor sale)

Question 54: The file P02_55xslx contains monthly retail sales of beer, wine, and liquor in US liquor stores.

a. Is seasonality present in these data? If so, characterize the seasonality pattern and then deseasonalize this time series using the ratio-to-moving average method.

b. If you decided to deseasonalize this time series in part **a** forecast the deseasonalized data for each month of the next year using the moving average method with an appropriate span.

c. Does Holt’s exponential smoothing method, with optimal smoothing constant, outperform the moving average method in part **b**? Demonstrate why or why not.

Professors note for 54: Part A, graph and talk about seasonality in the data.

Part C, just use the measures of forecast accuracy you have cited.

**Note**: You may ** not** use the ratio-to-moving-average with Winters' Model, at the same time.

55 (refers to P02_55) Winters’ method (beer/wine/liquor sale)

Question 55: Continuing the previous problem, how do your responses to the questions change if you employ Winter’s method to handle seasonality in this time series? Explain. Which forecasting method do you prefer, Winter’s Method or one of the methods used in the previous problem? Defend your choice.

Subject | Mathematics |

Due By (Pacific Time) | 06/21/2013 11:59 pm |

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