Bryan Caplan
bcaplan@gmu.edu
http://www.gmu.edu/departments/economics/bcaplan
Econ 637
Spring, 1999
Week 10: Time Series, I: The Basics
Process Name |
Nonstationary? |
Explosive? |
Example |
Solution |
Stationary |
No |
No |
Y_{t}=1+.95Y_{t-1}+u_{t} |
none needed |
Trend stationary |
Yes |
No |
Y_{t}=1+.9Y_{t-1}+5t+u_{t} |
first difference as: D Y_{t}=50+D u_{t} |
Random walk with drift |
Yes |
No |
Y_{t}=a+Y_{t-1}+u_{t}. |
first difference as: D Y_{t}=a+u_{t.} |
Explosive |
Yes |
Yes |
Y_{t}=1+1.05Y_{t-1}+u_{t} |
Hard: Differencing won't work |
Random walk with drift and trend |
Yes |
No |
Y_{t}=1+Y_{t-1}+5t+u_{t} |
Difference twice to get: D Y_{t}-D Y_{t-1}=5+D u_{t} |
Appendix: GLS, Heteroscedasticity, and Autocorrelation