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Exam 18: Time Series and Forecasting

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Exam 1: Statistics and Data100 Questionsadd course
Exam 2: Tabular and Graphical Methods123 Questionsadd course
Exam 3: Numerical Descriptive Measures151 Questionsadd course
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Exam 16: Regression Models for Nonlinear Relationships115 Questionsadd course
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Exam 18: Time Series and Forecasting124 Questionsadd course
Exam 19: Returns, Index Numbers and Inflation120 Questionsadd course
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Based on quarterly data collected over the last four years,the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook: Based on quarterly data collected over the last four years,the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook: = 3,305 - 665Qtr1 - 1,335Qtr2 + 305Qtr3,where Qtr1,Qtr2,and Qtr3 are dummy variables corresponding to Quarters 1,2,and 3. Which of the following is not true? = 3,305 - 665Qtr1 - 1,335Qtr2 + 305Qtr3,where Qtr1,Qtr2,and Qtr3 are dummy variables corresponding to Quarters 1,2,and 3. Which of the following is not true?

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Question 101

The model The model = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + ε<sub>t </sub>is known as a(n)_______. = β0 + β1yt - 1 + εt is known as a(n)_______.

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Question 102

The following table shows the annual revenues (in millions of dollars)of a pharmaceutical company over the period 1990-2011. 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,y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + ε<sub>t</sub>,and y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + β<sub>2</sub>y<sub>t - 2</sub> + ε<sub>t</sub>,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): When for AR(1),H<sub>0</sub>: β<sub>0</sub> = 0 is tested against H<sub>A</sub>: β<sub>0</sub> ≠ 0,the p-value of this t test shown by Excel output is 0.9590.This could suggest that the model y<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1 </sub>+ ε<sub>t</sub> might be an alternative to the AR(1)model y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>.Excel partial output for this simplified model is as follows: (Use Regression in Data Analysis of Excel. ) Compare the autoregressive models y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>;y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + β<sub>2</sub>y<sub>t</sub><sub>-2 </sub>+ ε<sub>t</sub>,andy<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + ε<sub>t</sub>,through the use of MSE and MAD. The autoregressive models of order 1 and 2,yt = β0 + β1yt - 1 + εt,and yt = β0 + β1yt - 1 + β2yt - 2 + εt,were applied on the time series to make revenue forecasts.The relevant parts of Excel regression outputs are given below. Model AR(1): 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,y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + ε<sub>t</sub>,and y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + β<sub>2</sub>y<sub>t - 2</sub> + ε<sub>t</sub>,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): When for AR(1),H<sub>0</sub>: β<sub>0</sub> = 0 is tested against H<sub>A</sub>: β<sub>0</sub> ≠ 0,the p-value of this t test shown by Excel output is 0.9590.This could suggest that the model y<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1 </sub>+ ε<sub>t</sub> might be an alternative to the AR(1)model y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>.Excel partial output for this simplified model is as follows: (Use Regression in Data Analysis of Excel. ) Compare the autoregressive models y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>;y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + β<sub>2</sub>y<sub>t</sub><sub>-2 </sub>+ ε<sub>t</sub>,andy<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + ε<sub>t</sub>,through the use of MSE and MAD. 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,y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + ε<sub>t</sub>,and y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + β<sub>2</sub>y<sub>t - 2</sub> + ε<sub>t</sub>,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): When for AR(1),H<sub>0</sub>: β<sub>0</sub> = 0 is tested against H<sub>A</sub>: β<sub>0</sub> ≠ 0,the p-value of this t test shown by Excel output is 0.9590.This could suggest that the model y<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1 </sub>+ ε<sub>t</sub> might be an alternative to the AR(1)model y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>.Excel partial output for this simplified model is as follows: (Use Regression in Data Analysis of Excel. ) Compare the autoregressive models y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>;y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + β<sub>2</sub>y<sub>t</sub><sub>-2 </sub>+ ε<sub>t</sub>,andy<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + ε<sub>t</sub>,through the use of MSE and MAD. Model AR(2): 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,y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + ε<sub>t</sub>,and y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + β<sub>2</sub>y<sub>t - 2</sub> + ε<sub>t</sub>,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): When for AR(1),H<sub>0</sub>: β<sub>0</sub> = 0 is tested against H<sub>A</sub>: β<sub>0</sub> ≠ 0,the p-value of this t test shown by Excel output is 0.9590.This could suggest that the model y<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1 </sub>+ ε<sub>t</sub> might be an alternative to the AR(1)model y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>.Excel partial output for this simplified model is as follows: (Use Regression in Data Analysis of Excel. ) Compare the autoregressive models y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>;y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + β<sub>2</sub>y<sub>t</sub><sub>-2 </sub>+ ε<sub>t</sub>,andy<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + ε<sub>t</sub>,through the use of MSE and MAD. 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,y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + ε<sub>t</sub>,and y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + β<sub>2</sub>y<sub>t - 2</sub> + ε<sub>t</sub>,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): When for AR(1),H<sub>0</sub>: β<sub>0</sub> = 0 is tested against H<sub>A</sub>: β<sub>0</sub> ≠ 0,the p-value of this t test shown by Excel output is 0.9590.This could suggest that the model y<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1 </sub>+ ε<sub>t</sub> might be an alternative to the AR(1)model y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>.Excel partial output for this simplified model is as follows: (Use Regression in Data Analysis of Excel. ) Compare the autoregressive models y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>;y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + β<sub>2</sub>y<sub>t</sub><sub>-2 </sub>+ ε<sub>t</sub>,andy<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + ε<sub>t</sub>,through the use of MSE and MAD. When for AR(1),H0: β0 = 0 is tested against HA: β0 ≠ 0,the p-value of this t test shown by Excel output is 0.9590.This could suggest that the model yt = β1yt-1 + εt might be an alternative to the AR(1)model yt = β0 + β1yt-1 + εt.Excel partial output for this simplified model is as follows: 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,y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + ε<sub>t</sub>,and y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + β<sub>2</sub>y<sub>t - 2</sub> + ε<sub>t</sub>,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): When for AR(1),H<sub>0</sub>: β<sub>0</sub> = 0 is tested against H<sub>A</sub>: β<sub>0</sub> ≠ 0,the p-value of this t test shown by Excel output is 0.9590.This could suggest that the model y<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1 </sub>+ ε<sub>t</sub> might be an alternative to the AR(1)model y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>.Excel partial output for this simplified model is as follows: (Use Regression in Data Analysis of Excel. ) Compare the autoregressive models y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>;y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + β<sub>2</sub>y<sub>t</sub><sub>-2 </sub>+ ε<sub>t</sub>,andy<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + ε<sub>t</sub>,through the use of MSE and MAD. 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,y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + ε<sub>t</sub>,and y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t - </sub><sub>1</sub> + β<sub>2</sub>y<sub>t - 2</sub> + ε<sub>t</sub>,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): When for AR(1),H<sub>0</sub>: β<sub>0</sub> = 0 is tested against H<sub>A</sub>: β<sub>0</sub> ≠ 0,the p-value of this t test shown by Excel output is 0.9590.This could suggest that the model y<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1 </sub>+ ε<sub>t</sub> might be an alternative to the AR(1)model y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>.Excel partial output for this simplified model is as follows: (Use Regression in Data Analysis of Excel. ) Compare the autoregressive models y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t-1</sub> + ε<sub>t</sub>;y<sub>t</sub> = β<sub>0 </sub>+ β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + β<sub>2</sub>y<sub>t</sub><sub>-2 </sub>+ ε<sub>t</sub>,andy<sub>t</sub> = β<sub>1</sub>y<sub>t</sub><sub>-1</sub> + ε<sub>t</sub>,through the use of MSE and MAD. (Use Regression in Data Analysis of Excel. ) Compare the autoregressive models yt = β0 + β1yt-1 + εt;yt = β0 + β1yt-1 + β2yt-2 + εt,andyt = β1yt-1 + εt,through the use of MSE and MAD.

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Question 103

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 three years: 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 three years: If the trend is described by the trend line = 1,000 + 30t,what is the forecast for the fourth quarter of this year? If the trend is described by the trend line 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 three years: If the trend is described by the trend line = 1,000 + 30t,what is the forecast for the fourth quarter of this year? = 1,000 + 30t,what is the forecast for the fourth quarter of this year?

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Question 104

Prices of crude oil have been steadily rising over the last two years (The Wall Street Journal,December 14,2010).The monthly data on price per gallon of unleaded regular gasoline in the United States from January 2009 to December 2010 were available.Three trend models were created,and the following relevant information became available. Prices of crude oil have been steadily rising over the last two years (The Wall Street Journal,December 14,2010).The monthly data on price per gallon of unleaded regular gasoline in the United States from January 2009 to December 2010 were available.Three trend models were created,and the following relevant information became available. Using the cubic trend equation,which of the following would be the forecast for the price of regular unleaded gasoline for January 2011? Using the cubic trend equation,which of the following would be the forecast for the price of regular unleaded gasoline for January 2011?

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Question 105

In which of the following situations is the use of qualitative forecasts most appropriate?

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Question 106

In the modelyt = β0 + β1yt-1 + εt,the parameter β1 represents the _____ of the lagged response variable y.

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Question 107

Which of the following types of trend models will best suit a series where the increase in value of the series gets larger over time?

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Question 108

Which of the following is not true of seasonal dummy variables?

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Question 109

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 110

The following table includes the information about a monthly time series. The following table includes the information about a monthly time series. What is the forecast for May using the exponential smoothing method with α = 0.5? What is the forecast for May using the exponential smoothing method with α = 0.5?

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Question 111

When a time series is analyzed by the model yt = Tt × St × It and the trend component Tt is set to be the centered moving average When a time series is analyzed by the model y<sub>t</sub> = T<sub>t</sub> × S<sub>t</sub> × I<sub>t</sub> 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 112

Which of the following models is assumed for a quarterly time series that seems to grow on average by an increasing amount (or decline by a decreasing amount)and seems to have seasonality?

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Question 113

In the exponential smoothing formula for updating the level of the series,At = αyt + (1 - α)At - 1,what does α represent?

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Question 114

The linear trend, The linear trend, = 660 + 2t,for seasonally adjusted monthly sales was estimated using a time series with monthly data from the last five years.Furthermore,the seasonal index for October was found to be 0.92.Which of the following is the forecast for the month of October of this year? = 660 + 2t,for seasonally adjusted monthly sales was estimated using a time series with monthly data from the last five years.Furthermore,the seasonal index for October was found to be 0.92.Which of the following is the forecast for the month of October of this year?

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Question 115

Based on quarterly data collected over the last five years,the following regression equation was found to forecast the quarterly demand for the number of new copies of a business statistics textbook: Based on quarterly data collected over the last five years,the following regression equation was found to forecast the quarterly demand for the number of new copies of a business statistics textbook: = 2,298 - 6635Qtr1 - 1,446Qtr2 + 303Qtr3 + 26t,where Qtr1,Qtr2,and Qtr3 are dummy variables corresponding to Quarters 1,,2 and 3,and t = time period. For a given year,the demand in Quarter 4 is on average ___________. = 2,298 - 6635Qtr1 - 1,446Qtr2 + 303Qtr3 + 26t,where Qtr1,Qtr2,and Qtr3 are dummy variables corresponding to Quarters 1,,2 and 3,and t = time period. For a given year,the demand in Quarter 4 is on average ___________.

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Question 116

The past monthly demands are shown below.The naïve method,that is,the one-period moving average method,is applied to make forecasts. The past monthly demands are shown below.The naïve method,that is,the one-period moving average method,is applied to make forecasts. What is the mean square error of the forecasts? What is the mean square error of the forecasts?

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Question 117

Based on quarterly data collected over the last four years,the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook: Based on quarterly data collected over the last four years,the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook: = 3,305 - 665Qtr1 - 1,335Qtr2 + 305Qtr3,where Qtr1,Qtr2,and Qtr3 are dummy variables corresponding to Quarters 1,2,and 3. By what percent is the demand in Quarter 3 higher on average than the average quarterly demand? = 3,305 - 665Qtr1 - 1,335Qtr2 + 305Qtr3,where Qtr1,Qtr2,and Qtr3 are dummy variables corresponding to Quarters 1,2,and 3. By what percent is the demand in Quarter 3 higher on average than the average quarterly demand?

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Question 118

When the exponential trend model is used to make forecasts,it is preferable to round the estimates b0,b1,and se in the equation When the exponential trend model is used to make forecasts,it is preferable to round the estimates b<sub>0</sub>,b<sub>1</sub>,and s<sub>e</sub> in the equation

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Question 119

If the model yt = Tt × St × It is applied,which of the following indicates no seasonality?

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Question 120
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