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

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

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

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

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

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

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

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

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