1. 1 Lab Five

2. 2 Dark Northern Spring Wheat Import price in dollars in Japan: dnsj Import price in dollars in Japan: dnsj

3. 3 Import Price !975:11 – 1981:10

4. 4 Identification Trace Trace Histogram Histogram Correlogram Correlogram Unit Root test Unit Root test

5. 5 Histogram

6. 6

7. 7

8. 8 First difference of DNSJ

9. 9 Histogram

10. 10

11. 11

12. 12 DNSPJT Export price in Dollars from Pacific Ports to Japan (lagged one) Plus the freight rate (lagged two) Export price in Dollars from Pacific Ports to Japan (lagged one) Plus the freight rate (lagged two)

13. 13

14. 14 Two random walks But they do not drift away from one another But they do not drift away from one another Difference = dnsj –dnspjt = japmminx Difference = dnsj –dnspjt = japmminx

15. 15

16. 16 Two random walks moving together

17. 17 Co-integrated time series

18. 18 Identifying their difference

19. 19Histogram

20. 20

21. 21

22. 22 Modeling the Difference

23. 23

24. 24 Validating the model

25. 25

26. 26 Validating the Model

27. 27

28. 28

29. 29 ARCH LM Test