Data Analysis and Economic Forecasting
Examination 2

These questions are from the test bank.  Some questions have multiple parts.

Theoretical Questions

 

1. You are forecasting future commodity prices, like gold and silver prices.  Describe a good method to check the accuracy of your forecast.

2. What is autocorrelation in terms of a linear regression model?

How can you detect an AR(1) process?

How do you correct for it?

How can you detect an AR(4) process?

How do you theoretically correct for it?

3. If autocorrelation or heteroscedasticity is present, what can you say about the parameter estimates, standard errors, t-statistics, and F-test from a regular Linear Regression that does not correct these problems?

4. What is a polynomial trend regression?

When do you stop adding terms to a polynomial trend regression?

5. What is heteroscedasticity?

How do you detect heteroscedasticity?

6. What is the Durbin-Watson Statistic?

Does it have limitations?

Please list a rough scale, when DW =0, DW = 2, and DW =4.

7. What is Ridge Regression?

When do you use it?

How do you change the least square estimator for b = (X TX) -1X TY.?

How do you choose values of l?

8. What is a composite forecast?

If you have two time series, X t and Y t, and their forecasts, how do you combine them together into one forecast?

How can you use Least Squares to improve the performance of a composite forecast?
     (Include in your discussion the constraints that are imposed on the weights).

9. How do econometricians define a stationary process?

Draw an example where a time series exhibits an I(0) process and its characteristic ACF plot.

Draw an example where a time series exhibits an I(1)  process and its characteristic ACF plot.

10. You have a program that can only estimate ARMA models.  However, you have data that is nonstationary of degree I(1).  How could you estimate this ARIMA by using an ARMA?

11. You have the ARMA(1,0) process, (1 - f B) X t = Z t. Please show the algebra to convert the AR process into an infinite series MA process

12. You have the ARIMA specification, (1 - f B)(1 - B) 1X t = (1 + q B)Z t.  Please write out the explicit expression for X t.

Empirical Questions


13. You forecasted the time-series below. Please calculate the Mean Squared Errors (MSE), Root Mean Squared Errors (RMSE), and Means Absolute Errors (MAE). Round numbers to the nearest tenth.

Year Actual Data Forecasts Error
2007 6.8 5.5  
2008 7.9 8.8  
2009 11.2 10.0  

Note - these formulas will be given to you on the exam.  You do not have to memorize them!

14. Please use a two-term Moving Average Forecast and a two-term Exponential Smoothing Forecast for the data below:  Round numbers to the nearest tenth.

Year Data, X t Moving Average
Forecast 		Forecasting
Error 		Exponential Smoothing
Forecast 		Forecasting
Error
2007 13.2      
2008 13.8      
2009 14.3      
2010      
2011      

Choose Alpha to be a = 0.5

Note - I will give you these two formulas on the exam.  You do not < have to memorize them!

15. Please calculate the Durbin-Watson statistic for the data below?

29.0     3.6     8.5    -0.7     -0.9

Does it appear that autocorrelation is present?

Note - I will give you the Durbin-Watson statistic formula on the exam.

16. You estimated the following ARMA model, .X t = 0.5 X t-1 +Z t + 0.5 Z t-1.  Please calculate its fit and forecasts below:

Year X i Forecast Residual
2007 5  
2008 2  
2009 5  
2010  
2011