**I- Download the quarterly data on CPI for the period 2004.1-2009.4, find the following estimates and do the following tests.**

1. Plot the variable over time. Explain the movements in your variable and mark the outliers and structural break, if any. Comment on the existence of time trend, seasonal trend, cyclical trend, and randomness in the variable.

2. Do the histogram of the CPI data and comment on the distribution of data.

3. Plot the natural logarithm of the variable. Explain movements in the natural log of the variable and mark the outliers and structural breaks.

4. Plot the histogram of the log of the variable and comment on its distribution.

5. Comment on the differences between the behavior of the variable and the natural log of the variable.

6. Find the summary statistics of the CPI variable.

7. Do a hypothesis test that the mean CPI during the 2004.1-2006.12 is statistically no different from the mean CPI during the 2007.1-2009.12.

8. Do a hypothesis test that the variation of CPI during the 2004.1-2006.12 is statistically no different from the mean CPI during the 2007.1-2009.12.

9. Create the lag of the CPI variable and use it as a naive forecast of your variable. Find the mean absolute deviation (MAD), mean absolute percentage error (MAPE), and mean squared error (MSE) for your forecast.

12. Divide the CPI data to three equal-size periods. Find the means and the variances of the first and the last periods.

13. Do a hypothesis test that the mean of the first period is the same as the mean of the third period.

14. Do a hypothesis testing that the variance of the first period is the same as the variance of the Third period.

15. Find the correlation coefficient between the first period and the third period data. Comment on the correlation coefficient.

16. Take time as an explanatory variable. Find the correlation between the CPI and the time. Comment on the correlation.

**II. - For the CPI variable find the following estimates and do the following tests.**

1. Plot a scatter diagram of the variable and comment on the time trend of the variable.

2. Run a regression of the CPI variable on time and analyze the relationship (Comment on the significance of the coefficients and overall explaining power of the regression).

3. Find the estimated value of the dependent variable (y-hat)

4. Graph the dependent variable (y) and the estimated y, (y-hat), on the same coordinate system and comment on the relationship between the two.

5. Find the histogram of the regression error. Comment on the distribution of the residuals.

6. Run a regression of the variable on a polynomial function on time and analyze the relationship. Fit the best model and decide on the degree of the polynomial.

7. Find the estimated value of the dependent variable (y-hat).

8. Graph the dependent variable (y) and the estimated y, (y-hat), on the same coordinate system and comment on the relationship between the two.

9. Find the MAD, MAPE, and RMSSE of the regression error.

10. Compare the MAD, MAPE, and RMSE of the two models.

11. Do a three period forecasting based on your best regression on time

12. Find an explanatory variable based on economic theory. Run a regression of the dependent variable on time and other explanatory variable.

13. Decide on the significance and efficiency of the best model.

14. Find the MAD, MAPE, and RMSE of the regression error.

Subject | Business |

Due By (Pacific Time) | 07/29/2013 08:00 am |

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