1. Some Important Time Series Processes Fin250f: Lecture 8.3 Spring 2010

2. Outline  Basic finance price dynamics Random walk Geometric random walk Martingale  Random walk + noise  Trend + noise

3. Random Walk

4. Geometric Random Walk

5. Martingale

6. Random Walk + Noise

7.  Why interesting?  Exponential smoother is the optimal forecast  History: Muth, and rational expectations

8. Trend + Noise Model  Model returns as Small persistent trend Plus noise  Can generate significant predictability which is invisible to most tests

9. Covariance Reminder

10. Trend + Noise

11. Trend Plus Noise

12. Parameter Example  A small   big  A = 0.02, 

13. Trend Plus Noise ACF

14. AR(1) ACF’s

15. Trend Plus Noise  Can show Returns are ARMA(1,1) ARMA’s can generate persistent, but small autocorrelations for certain parameters  This is useful to model returns Low correlations Trends for momentum/moving average trading rules