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Exam 18: Time Series and Forecasting

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Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.What is a revenue forecast for 2012 found by the exponential trend equation? Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.What is a revenue forecast for 2012 found by the exponential trend equation? Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.What is a revenue forecast for 2012 found by the exponential trend equation? Refer to Exhibit 18.3.What is a revenue forecast for 2012 found by the exponential trend equation?

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Question 21

Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.What is the revenue forecast for 2013 found by the trend regression equation with the best fit? Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.What is the revenue forecast for 2013 found by the trend regression equation with the best fit? Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.What is the revenue forecast for 2013 found by the trend regression equation with the best fit? Refer to Exhibit 18.3.What is the revenue forecast for 2013 found by the trend regression equation with the best fit?

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Question 22

Exhibit 18.7.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Exhibit 18.7.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, and ,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): Model AR(2): Refer to Exhibit 18.7.(Use Regression in Data Analysis of Excel. )Compare the autoregressive models, and ,through the use of MSE and MAD.Hint.You may compute the errors by clicking Residuals;to analyze instead of ,it suffices to click Constant is Zero. The autoregressive models of order 1 and 2, Exhibit 18.7.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, and ,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): Model AR(2): Refer to Exhibit 18.7.(Use Regression in Data Analysis of Excel. )Compare the autoregressive models, and ,through the use of MSE and MAD.Hint.You may compute the errors by clicking Residuals;to analyze instead of ,it suffices to click Constant is Zero. and Exhibit 18.7.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, and ,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): Model AR(2): Refer to Exhibit 18.7.(Use Regression in Data Analysis of Excel. )Compare the autoregressive models, and ,through the use of MSE and MAD.Hint.You may compute the errors by clicking Residuals;to analyze instead of ,it suffices to click Constant is Zero. ,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): Exhibit 18.7.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, and ,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): Model AR(2): Refer to Exhibit 18.7.(Use Regression in Data Analysis of Excel. )Compare the autoregressive models, and ,through the use of MSE and MAD.Hint.You may compute the errors by clicking Residuals;to analyze instead of ,it suffices to click Constant is Zero. Model AR(2): Exhibit 18.7.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, and ,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): Model AR(2): Refer to Exhibit 18.7.(Use Regression in Data Analysis of Excel. )Compare the autoregressive models, and ,through the use of MSE and MAD.Hint.You may compute the errors by clicking Residuals;to analyze instead of ,it suffices to click Constant is Zero. Refer to Exhibit 18.7.(Use Regression in Data Analysis of Excel. )Compare the autoregressive models, Exhibit 18.7.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, and ,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): Model AR(2): Refer to Exhibit 18.7.(Use Regression in Data Analysis of Excel. )Compare the autoregressive models, and ,through the use of MSE and MAD.Hint.You may compute the errors by clicking Residuals;to analyze instead of ,it suffices to click Constant is Zero. and Exhibit 18.7.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, and ,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): Model AR(2): Refer to Exhibit 18.7.(Use Regression in Data Analysis of Excel. )Compare the autoregressive models, and ,through the use of MSE and MAD.Hint.You may compute the errors by clicking Residuals;to analyze instead of ,it suffices to click Constant is Zero. ,through the use of MSE and MAD.Hint.You may compute the errors by clicking "Residuals";to analyze Exhibit 18.7.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, and ,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): Model AR(2): Refer to Exhibit 18.7.(Use Regression in Data Analysis of Excel. )Compare the autoregressive models, and ,through the use of MSE and MAD.Hint.You may compute the errors by clicking Residuals;to analyze instead of ,it suffices to click Constant is Zero. instead of Exhibit 18.7.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, and ,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): Model AR(2): Refer to Exhibit 18.7.(Use Regression in Data Analysis of Excel. )Compare the autoregressive models, and ,through the use of MSE and MAD.Hint.You may compute the errors by clicking Residuals;to analyze instead of ,it suffices to click Constant is Zero. ,it suffices to click "Constant is Zero".

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Question 23

If T denotes the number of observations,which of the following equations represents the one-step-ahead forecast for the model If T denotes the number of observations,which of the following equations represents the one-step-ahead forecast for the model ? ?

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Question 24

Exhibit 18.1.The past monthly demands are shown below.The naïve method,that is,the one-period moving average method,is applied to make forecasts. Exhibit 18.1.The past monthly demands are shown below.The naïve method,that is,the one-period moving average method,is applied to make forecasts. Refer to Exhibit 18.1.If May's demand appears to be 35,what is the residual (error)for May? Refer to Exhibit 18.1.If May's demand appears to be 35,what is the residual (error)for May?

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Question 25

Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.What is the revenue forecast for 2012 found by the linear trend equation? Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.What is the revenue forecast for 2012 found by the linear trend equation? Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.What is the revenue forecast for 2012 found by the linear trend equation? Refer to Exhibit 18.3.What is the revenue forecast for 2012 found by the linear trend equation?

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Question 26

Exhibit 18.4.The following ratio-to-moving averages for the seasonally adjusted series were found by the decomposition method applied on a time series representing quarterly sales for the last four years: Exhibit 18.4.The following ratio-to-moving averages for the seasonally adjusted series were found by the decomposition method applied on a time series representing quarterly sales for the last four years: Refer to Exhibit 18.4.By how many percent the sales in Quarter 4 exceed the average quarterly sales? Refer to Exhibit 18.4.By how many percent the sales in Quarter 4 exceed the average quarterly sales?

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Question 27

Under which of the following conditions is qualitative forecasting considered attractive?

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Question 28

When a time series is analyzed by the model When a time series is analyzed by the model and the trend component T<sub>t</sub> is set to be the centered moving average ,which of the following remains to be estimated? and the trend component Tt is set to be the centered moving average When a time series is analyzed by the model and the trend component T<sub>t</sub> is set to be the centered moving average ,which of the following remains to be estimated? ,which of the following remains to be estimated?

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Question 29

When comparing which of the following trend models is the adjusted When comparing which of the following trend models is the adjusted not used? not used?

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Question 30

Exhibit 18.5.Based on quarterly data collected over the last 4 years,the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook: Exhibit 18.5.Based on quarterly data collected over the last 4 years,the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook: , where Qtr1,Qtr2 and Qtr3 are dummy variables corresponding to Quarters 1,2 and 3. Refer to Exhibit 18.5.Which of the following is not true? , where Qtr1,Qtr2 and Qtr3 are dummy variables corresponding to Quarters 1,2 and 3. Refer to Exhibit 18.5.Which of the following is not true?

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Question 31

Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.When three polynomial trend equations are compared,which of them provides the best fit? Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.When three polynomial trend equations are compared,which of them provides the best fit? Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Exhibit 18.3.The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. Excel scatterplot shown above indicates that the annual revenues have an increasing trend.Therefore,linear,exponential,quadratic and cubic models were used to fit the trend,and the following relevant information became available after applying linear regression. Refer to Exhibit 18.3.When three polynomial trend equations are compared,which of them provides the best fit? Refer to Exhibit 18.3.When three polynomial trend equations are compared,which of them provides the best fit?

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Question 32

In forecasting methods,the mean square error (MSE)is computed by dividing the sum of squared residuals (errors)by the number of observations n for which the residuals are available.

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Question 33

When a time series has both trend and seasonality,moving averages can be employed to separate the effect of these two components.

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Question 34

Which of the following is not a criticism made of qualitative forecasts?

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Question 35

Using the decomposition model Using the decomposition model ,forecasts are made by _______,where and represent the estimated trend and the (adjusted)seasonal index for period t,respectively. ,forecasts are made by _______,where Using the decomposition model ,forecasts are made by _______,where and represent the estimated trend and the (adjusted)seasonal index for period t,respectively. and Using the decomposition model ,forecasts are made by _______,where and represent the estimated trend and the (adjusted)seasonal index for period t,respectively. represent the estimated trend and the (adjusted)seasonal index for period t,respectively.

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Question 36

Exhibit 18.5.Based on quarterly data collected over the last 4 years,the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook: Exhibit 18.5.Based on quarterly data collected over the last 4 years,the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook: , where Qtr1,Qtr2 and Qtr3 are dummy variables corresponding to Quarters 1,2 and 3. Refer to Exhibit 18-5.The demand forecast for Quarter 2 of the next year is , where Qtr1,Qtr2 and Qtr3 are dummy variables corresponding to Quarters 1,2 and 3. Refer to Exhibit 18-5.The demand forecast for Quarter 2 of the next year is

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Question 37

While we use the mean square error (MSE)to compare the linear and the exponential trend models,we cannot use it to compare the linear,quadratic,and cubic trend models.

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Question 38

Exhibit 18.6.Based on quarterly data collected over the last 5 years,the following regression equation was found to forecast the quarterly demand for the number of new copies of a business statistics textbook: Exhibit 18.6.Based on quarterly data collected over the last 5 years,the following regression equation was found to forecast the quarterly demand for the number of new copies of a business statistics textbook: , where Qtr1,Qtr2 and Qtr3 are dummy variables corresponding to Quarters 1,2 and 3,and t = time period. Refer to Exhibit 18.6.For a given year,the demand in Quarter 3 is on average , where Qtr1,Qtr2 and Qtr3 are dummy variables corresponding to Quarters 1,2 and 3,and t = time period. Refer to Exhibit 18.6.For a given year,the demand in Quarter 3 is on average

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Question 39

Which of the following is true of the linear trend model?

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Question 40
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