1. MEASURING EFFICIENCY OF INTERNATIONAL CRUDE OIL MARKETS: A MULTIFRACTALITY APPROACH Harvey M. Niere Department of Economics Mindanao State University Philippines

2. Fractal System A system characterised by a scaling law with a fractal, i. e., non- integer exponent. Fractal systems are characterised by self-similarity, i. e., a magnification of a small part is statistically equivalent to the whole. (Kantelhardt 2008)

3. Fractals

4. Fractals

5. Koch Snowflakes

6. Mandelbrot set Iterated Function Systems:

13. sea shells

14. lightning

15. trees

16. leaves

17. rivers

18. mountain ranges

20. multi-level marketing

21. time series data

22. Multifractal System A system characterised by scaling laws with an infinite number of different fractal exponents. The scaling laws must be valid for the same range of the scale parameter. (Kantelhardt 2008)

23. Multifractal System According to Zunino et al. (2008), multifractality can be due 1.long-range correlations or 2.broad fat-tail distributions

24. Multifractal System Mandelbrot (1997) introduced multifractal models to study economic and financial time series in order to address the shortcomings of traditional models such as fractional Brownian motion and GARCH processes which are not appropriate with the stylized facts of the said time series such as long-memory and fat-tails in volatility.

25. Ihlen (2012)

26. Fractals, Multifractals and Hurst Exponent For fractals, the Hurst exponent,h, is constant. Ordinary Brownian motion, h = 0.5 Fractional Brownian motion, 0 < h < 1 For multifractals, the Hurst exponent is not constant but is dependent with the order of fluctuation function, q. In this case, h(q), is known as the generalized Hurst exponent. If q = 2, then h(2) = h.

27. Market Efficiency This refers to the degree in which the price reflects the all the available information about the asset. If the market is efficient, then the price movement follows a random walk behavior. In this case, the price movement is just an ordinary Brownian motion with h = 0.5.

28. Methodology

29. Methodology

30. Methodology

31. Methodology

32. Methodology

33. Methodology

34. Data The daily prices of Brent crude, OPEC reference basket and West Texas Intermediate (WTI) crude from January 2, 2003 to January 2, 2014 are used. The number of observations are 2788, 2839 and 2765 for Brent crude, OPEC reference basket and West Texas Intermediate (WTI) crude respectively. The data for Brent crude and West Texas Intermediate (WTI) crude are downloaded from the US Energy Information Administration online database website: http://www.eia.gov/dnav/pet/pet_pri_spt_s1_d.htm. http://www.eia.gov/dnav/pet/pet_pri_spt_s1_d.htm The data for OPEC reference basket are downloaded from the OPEC online database website: http://www.opec.org/opec_web/en/data_graphs/40.htm http://www.opec.org/opec_web/en/data_graphs/40.htm

36. Brent Crude

37. OPEC Reference Basket

38. WTI Crude

39. Brent Crude

40. OPEC Reference Basket

41. WTI Crude

43. Results BrentOPECWTI OriginalShuffledSurrogatedOriginalShuffledSurrogatedOriginalShuffledSurrogated -10 0.49910.54270.5750 0.54960.53370.6397 0.49280.54100.5380 -9 0.49740.54120.5742 0.54770.53220.6387 0.49130.53930.5375 -8 0.49570.53970.5734 0.54580.53070.6377 0.48970.53740.5369 -7 0.49400.53810.5727 0.54390.52910.6367 0.48820.53550.5365 -6 0.49230.53650.5720 0.54200.52760.6358 0.48670.53360.5361 -5 0.49070.53490.5713 0.54010.52600.6350 0.48520.53160.5357 -4 0.48920.53330.5707 0.53820.52440.6342 0.48370.52960.5354 -3 0.48780.53160.5702 0.53650.52280.6334 0.48230.52760.5353 -2 0.48650.53000.5697 0.53490.52120.6328 0.48100.52550.5352 0.48540.52840.5692 0.53340.51970.6322 0.47980.52340.5352 0 0.48460.52680.5689 0.53220.51810.6318 0.47880.52130.5353 1 0.48410.52510.5686 0.53130.51650.6315 0.47810.51910.5356 2 0.48410.52350.5684 0.53090.51500.6312 0.47780.51700.5360 3 0.48460.52190.5682 0.53120.51350.6311 0.47790.51480.5365 4 0.48600.52030.5681 0.53220.51200.6312 0.47860.51270.5371 5 0.48830.51870.5681 0.53430.51050.6313 0.48010.51050.5378 6 0.49170.51710.5682 0.53790.50910.6316 0.48260.50830.5387 7 0.49670.51560.5683 0.54320.50760.6320 0.48640.50610.5396 8 0.50340.51400.5685 0.55080.50620.6324 0.49190.50380.5406 9 0.51220.51230.5687 0.56110.50470.6329 0.49930.50160.5416 10 0.52310.51070.5689 0.57430.50320.6335 0.50870.49930.5427 0.53600.50900.5691 0.59040.50170.6341 0.52000.49700.5437

44. Conclusions The study concludes that 1.Among the three major international crude oil markets under the study, WTI is the most efficient while OPEC is the most inefficient, and 2.for the three markets, the multifractality is mainly due to long-range correlation.

45. Thank you!