1. Introduction to Financial Time Series From Ruey. S. Tsay’s slides

2. What is Financial Time Series Analysis Theory and practice of asset valuation over time. Different from other T.S. analysis? Close, but with some added uncertainty. For example, FTS must deal with the ever- changing business & economic environment and the fact that volatility is not directly observed.

3. Examples of financial time series Daily log returns of GE stock Quarterly earnings of Johnson & Johnson  Seasonal time series useful in earning forecasts pricing weather related derivatives (e.g. energy) modeling intraday behavior of asset returns US monthly interest rates  Relations between the two series? Term structure of interest rates Exchange rate between US Dollar vs Japanese Yen  Fixed income, hedging, carry trade Size of insurance claims  Values of fire insurance claims from 1972 to 1992. High-frequency financial data:  Tick-by-tick data of Boeing stock: December 5, 2005.

4. Example of FTS

5. Example of FTS (Cont.)

6. Objective of the Course Provide some basic knowledge of financial time series data. Introduce some statistical tools & econometric models useful for analyzing these series. Gain empirical experience in analyzing FTS. Design your own method to predict future FTS.

7. Asset Returns From Ruey. S. Tsay’s slides

8. Asset Returns

9. Asset Return Example

10. Asset Returns

11. Compound Assert Returns

14. Asset Returns Pt: The price of an asset at time index t. One-period simple return, from t-1 to t Multi-period simple return, from t-k to t  Annualized Continuously compounded return

15. Asset Returns For multi-period returns, we have Captial Asset Price Model (CAPM):  Consider the joint distribution of N return at a single time index t, Or, study the distribution We will focus on the dynamic structure of individual asset returns, in other words, we study the distribution of How to describe the joint distribution of

16. Asset Returns For discrete case: For continuous case:

17. Marginal Distribution of Asset Returnd When asset returns have weak empirical serial correlation, their marginal distributions are close to their conditional distributions. Thus the question is how to estimate marginal distributions. Several statistical distributions have been proposed for marginal distribution of asset returns:  Normal distribution  Lognormal distribution  Stable distribution  Scale-Mixture Normal distribution

18. Linear Time Series Analysis From Ruey. S. Tsay’s slides

19. Linear Time Series (TS) Models

20. Basic Concepts

21. Basic Concepts (Cont.)

25. Univariate TS Analysis Purpose:

26. Example of Linear Time Series

27. Linear Financial Time Series

28. AR Model

29. AR Model (Cont.)

32. AR(2) Model

33. Building an AR Model

34. Moving-Average (MA) Model

35. MA(1) Model (Cont.)

36. MA(2) Model

37. Building MA Model

38. Mixed ARMA Model

39. Mixed ARMA Model (Cont.)

40. Building an ARMA (1, 1) Model

41. Three Model Comparisons:

42. Seasonal Time Series

43. Examples of Seasonal Time Series (1) Figure 1: Time plot of electricity demand of an industrial sector: 15th day of each month from1972 to 1993.

44. Example of Seasonal Time Series (2)

45. Example of Seasonal Time Series (3) Figure 3: Time plot of quarterly logged earnings of Johnson and Johnson: 1960-1980

46. Seasonal Difference Model