1. Time Series Basics Fin250f: Lecture 3.1 Fall 2005 Reading: Taylor, chapter 3.1-3.3

2. Outline  Random variables  Distributions  Central limit theorem  Two variables  Independence  Time series definitions

3. Random Variables: Discrete

4. Random Variables: Continuous

7. Important Distributions  Uniform  Normal  Log normal  Student-t  Stable

8. Normal/Gaussian

9. Normal Picture: Sample = 2000

10. Normal Exponential Expectations

11. Why Important in Finance?  Central limit theorem  Many returns almost normal

12. Log Normal

13.  Not symmetric  Long right tail

14. Log Normal Histogram (Sample = 5000)

15. Chi-square

16. Student-t

17. Student-t Moments  All moments > r do not exist

18. Stable Distribution  Similar shape to normal  Infinite variance  Sums of stable RV’s are stable

19. Central Limit Theorem (casual)

20. Consequence of CLT and continuous compounding

21. Two Variables

22. More on Two Variables

23. More Two Variables

24. Independent Random Variables

25. More than Two RV’s

26. Multivariate Normal

27. Independence

28. Independent Identically Distributed  All random variables drawn from same distribution  All are independent of each other  Common assumption  IID  IID Gaussian

29. Stochastic Processes

30. Time Series Definitions  Strictly stationary  Covariance stationary  Uncorrelated  White noise  Random walk  Martingale

31. Strictly Stationary  All distributional features are independent of time

32. Covariance Stationary  Variances and covariances independent of time

33. Uncorrelated

34. White Noise  Covariance stationary  Uncorrelated  Mean zero

35. Random Walk

36. Geometric Random Walk

37. Martingale

38. Autocovariances/correlations

39. Outline  Random variables  Distributions  Central limit theorem  Two variables  Independence  Time series definitions