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The Following Table Shows the Annual Revenues (In Millions of Dollars)of

Question 103

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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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