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  1. Bayesian modeling and analysis of stochastic volatility in finance Derrick Hang April 6, 2010 Economics 201FS

  2. Review from Last Time Regress for Prices: Possible useful predictors of prices are lost when we take the difference between prices to obtain returns In general , we expect

  3. Addressing Stationarity Concerns Classic tests for stationarity of an AR time series (i.e. Dickey-Fuller, Phillips-Peron, etc.) test the coefficient on the lagged time-series for a unit root However, these tests assume a CONSTANT coefficient and have LOW POWER DLM allows for the possibility of “pockets of stationarity” and will reject unit root null at values close to 1 Does stationarity of a model matter if we are looking for short term forecasting?

  4. The Data Jan 2, 2009 – June 31, 2009 (excluding April 10th) Data for market hours only (no weekend) : 9:35AM – 3:55PM 5 Minute Data (9778 total points for each dataset) All prices logged 10 dependent variable (USD/variable): AUD, CHF, EUR, GBP, JPY, NZD, CAD, NOK, SGD, ZAR 12 independent variable: 10 lagged forex variables, brent oil futures, comex gold futures Focus on AUD, GBP, JPY, brent, gold

  5. Back to Basics: Jump Testing What is the relationship –if any- between jump days and periods of non-unit roots?

  6. Back to Basics: Jump Testing

  7. Back to Basics: Jump Testing

  8. Back to Basics: Jump Testing

  9. Back to Basics: Jump Testing • 0.1% Significance Level = 25 / 127 (2.23%) • 1% Significance Level = 6 / 127 (4.72%) • 5% Significance Level = 1 / 127 (19.69%)

  10. Back to Basics: Jump Testing • 0.1% Significance Level = 5 / 127 (3.94%) • 1% Significance Level = 11/ 127 (8.66%) • 5% Significance Level = 24/ 127 (18.90%)

  11. Back to Basics: Jump Testing • 0.1% Significance Level = 3 / 127 (2.36%) • 1% Significance Level = 15/ 127 (11.81%) • 5% Significance Level = 38/ 127 (25.98%)

  12. Time-Varying Coefficient: Lagged GBP, JPY

  13. Time-Varying Coefficient: Brent, Gold

  14. Time-Varying Coefficient: Lagged AUD

  15. Start End • 03-Jun-2009 09:40:00 11-Jun-2009 14:55:00 • 14-Jan-2009 09:35:00 20-Jan-2009 15:55:00 • 18-Mar-2009 10:50:00 23-Mar-2009 15:55:00 • 30-Mar-2009 09:35:00 02-Apr-2009 13:25:00 • 25-Jun-2009 09:40:00 29-Jun-2009 15:55:00 • 22-Jun-2009 09:35:00 24-Jun-2009 15:00:00 • 08-Apr-2009 09:35:00 13-Apr-2009 12:45:00 • 10-Mar-2009 10:25:00 12-Mar-2009 13:00:00 • 27-Jan-2009 09:35:00 28-Jan-2009 15:55:00 • 09-Feb-2009 09:50:00 10-Feb-2009 15:55:00 • 19-Feb-2009 11:00:00 20-Feb-2009 14:45:00 • 12-Jun-2009 14:25:00 16-Jun-2009 10:55:00 • 06-Mar-2009 13:35:00 10-Mar-2009 09:50:00 • 17-Apr-2009 14:15:00 20-Apr-2009 14:25:00 • 30-Jan-2009 09:35:00 02-Feb-2009 09:35:00 Significant Windows: Lagged AUD (descending order)

  16. Jump Days: AUD (5% level) 08-Jan-2009 09:40:00 16-Jan-2009 09:40:00 28-Jan-2009 09:40:00 02-Feb-2009 09:40:00 03-Feb-2009 09:40:00 04-Feb-2009 09:40:00 23-Feb-2009 09:40:00 (03-Mar-2009 09:40:00) 12-Mar-2009 09:40:00 23-Mar-2009 09:40:00 31-Mar-2009 09:40:00 01-Apr-2009 09:40:00 13-Apr-2009 09:40:00 15-Apr-2009 09:40:00 16-Apr-2009 09:40:00 • 01-May-2009 09:40:00 • 08-May-2009 09:40:00 • 15-May-2009 09:40:00 • 20-May-2009 09:40:00 • 22-May-2009 09:40:00 • 02-Jun-2009 09:40:00 • 04-Jun-2009 09:40:00 • 05-Jun-2009 09:40:00 • 10-Jun-2009 09:40:00 • 11-Jun-2009 09:40:00

  17. Jump Days: AUD (1% and 0.1% level) 1% 08-Jan-2009 09:40:00 12-Mar-2009 09:40:00 13-Apr-2009 09:40:00 15-May-2009 09:40:00 22-May-2009 09:40:00 04-Jun-2009 09:40:00 0.1% 04-Jun-2009 09:40:00

  18. Start End • 30-Mar-2009 09:35:00 01-Apr-2009 13:20:00 • 03-Mar-2009 09:35:00 05-Mar-2009 11:05:00 • 10-Mar-2009 12:20:00 12-Mar-2009 13:00:00 • 26-Jun-2009 11:00:00 29-Jun-2009 15:55:00 • 29-Jan-2009 09:45:00 30-Jan-2009 13:50:00 • 27-Jan-2009 09:35:00 28-Jan-2009 09:55:00 • 19-Feb-2009 14:30:00 20-Feb-2009 14:45:00 • 17-Apr-2009 14:15:00 20-Apr-2009 14:25:00 • 06-Mar-2009 15:50:00 09-Mar-2009 15:55:00 Significant Windows: Lagged AUD, GBP, JPY (descending order)

  19. Jump Days: AUD (5% level) 08-Jan-2009 09:40:00 16-Jan-2009 09:40:00 28-Jan-2009 09:40:00 02-Feb-2009 09:40:00 03-Feb-2009 09:40:00 04-Feb-2009 09:40:00 23-Feb-2009 09:40:00 03-Mar-2009 09:40:00 12-Mar-2009 09:40:00 23-Mar-2009 09:40:00 31-Mar-2009 09:40:00 01-Apr-2009 09:40:00 13-Apr-2009 09:40:00 15-Apr-2009 09:40:00 16-Apr-2009 09:40:00 • 01-May-2009 09:40:00 • 08-May-2009 09:40:00 • 15-May-2009 09:40:00 • 20-May-2009 09:40:00 • 22-May-2009 09:40:00 • 02-Jun-2009 09:40:00 • 04-Jun-2009 09:40:00 • 05-Jun-2009 09:40:00 • 10-Jun-2009 09:40:00 • 11-Jun-2009 09:40:00

  20. Jump Days: AUD (1% and 0.1% level) 1% 08-Jan-2009 09:40:00 12-Mar-2009 09:40:00 13-Apr-2009 09:40:00 15-May-2009 09:40:00 22-May-2009 09:40:00 04-Jun-2009 09:40:00 0.1% 04-Jun-2009 09:40:00

  21. Start End • 30-Mar-2009 09:35:00 02-Apr-2009 09:35:00 • 19-Mar-2009 11:10:00 23-Mar-2009 14:30:00 • 10-Mar-2009 10:25:00 12-Mar-2009 13:00:00 Significant Windows: Lagged AUD, Brent, Gold (descending order)

  22. Jump Days: AUD (5% level) 08-Jan-2009 09:40:00 16-Jan-2009 09:40:00 28-Jan-2009 09:40:00 02-Feb-2009 09:40:00 03-Feb-2009 09:40:00 04-Feb-2009 09:40:00 23-Feb-2009 09:40:00 03-Mar-2009 09:40:00 12-Mar-2009 09:40:00 23-Mar-2009 09:40:00 31-Mar-2009 09:40:00 01-Apr-2009 09:40:00 13-Apr-2009 09:40:00 15-Apr-2009 09:40:00 16-Apr-2009 09:40:00 • 01-May-2009 09:40:00 • 08-May-2009 09:40:00 • 15-May-2009 09:40:00 • 20-May-2009 09:40:00 • 22-May-2009 09:40:00 • 02-Jun-2009 09:40:00 • 04-Jun-2009 09:40:00 • 05-Jun-2009 09:40:00 • 10-Jun-2009 09:40:00 • 11-Jun-2009 09:40:00

  23. Jump Days: AUD (1% and 0.1% level) 1% 08-Jan-2009 09:40:00 12-Mar-2009 09:40:00 13-Apr-2009 09:40:00 15-May-2009 09:40:00 22-May-2009 09:40:00 04-Jun-2009 09:40:00 0.1% 04-Jun-2009 09:40:00

  24. Initial Findings From the data so far, we have seen that the largest windows contain days declared as jump days Most of the time, windows that contain entire days have a “jump day” inside it Windows where multiple regressors are significant also contain declared jump days What does this all mean?

  25. Further Research Look to see if the relationship between large windows and jump days exist with the other dependent currency datasets Short term forecasts inside this windows? Try with different jump tests (other than Mean-adjusted TP) Fix bugs in code